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  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_trtn_ImpairmentAxis_e551c47e-6a74-4afe-947d-8f286f6d4b1d_terseLabel_en-US" xlink:label="lab_trtn_ImpairmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment [Axis]</link:label>
    <link:label id="lab_trtn_ImpairmentAxis_label_en-US" xlink:label="lab_trtn_ImpairmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment [Axis]</link:label>
    <link:label id="lab_trtn_ImpairmentAxis_documentation_en-US" xlink:label="lab_trtn_ImpairmentAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ImpairmentAxis" xlink:href="trtn-20241231.xsd#trtn_ImpairmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ImpairmentAxis" xlink:to="lab_trtn_ImpairmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_f2f8cb1b-cc6c-46de-8f20-ae6b442a87ef_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income (loss) to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetInterestCarryforward_0a490e06-75ef-47f4-beeb-34a83b724ffd_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset, interest carryforward</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetInterestCarryforward_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Interest Carryforward</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetInterestCarryforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:to="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_f582e900-7c4f-402d-82de-7ccbdef09a0a_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_bd8a3434-5954-4627-97e9-6a969b1b4abf_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_e1d75a09-6618-4dc2-9c39-dc9770e6e894_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet_cdb976e8-b6ee-4947-917e-9814aea804ef_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings under debt facilities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Long-Term Debt and Capital Securities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebtAndCapitalSecuritiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_e938e40b-03c5-4920-a14f-6ed4a0fdb157_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_112e5f5b-25db-46d3-a82b-d9771a76849f_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_f4e84e94-a00c-4e60-b852-a7d7fe32da94_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_5abe2b5e-3604-4915-9c56-86e7f83e758c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Maturity</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CashCollateralforInterestRateSwapContracts_3fea74f8-3994-48e2-8dd0-0652763bc2ce_terseLabel_en-US" xlink:label="lab_trtn_CashCollateralforInterestRateSwapContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral for interest rate swap contracts</link:label>
    <link:label id="lab_trtn_CashCollateralforInterestRateSwapContracts_label_en-US" xlink:label="lab_trtn_CashCollateralforInterestRateSwapContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Collateral for Interest Rate Swap Contracts</link:label>
    <link:label id="lab_trtn_CashCollateralforInterestRateSwapContracts_documentation_en-US" xlink:label="lab_trtn_CashCollateralforInterestRateSwapContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash Collateral for Interest Rate Swap Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CashCollateralforInterestRateSwapContracts" xlink:href="trtn-20241231.xsd#trtn_CashCollateralforInterestRateSwapContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CashCollateralforInterestRateSwapContracts" xlink:to="lab_trtn_CashCollateralforInterestRateSwapContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_6d454f92-13ff-40de-8fc4-4ec4345e6f94_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_8b0a30d2-1f8e-429a-82dd-2feafd273069_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_5e3b2d25-d06c-4f9a-862c-9a5b7c281393_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">7.625% Series F Cumulative Redeemable Perpetual Preference Shares</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series F Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesFPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeriesFPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesFPreferredStockMember" xlink:to="lab_us-gaap_SeriesFPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateAgreements_af978b47-e0ca-42dd-8e43-32b8df1f9d51_terseLabel_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount (in millions)</link:label>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateAgreements_label_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Notional Amount of Interest Rate Agreements</link:label>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateAgreements_documentation_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The net notional amount of interest rate swap/cap agreements, which relate to the currency amounts specified in the related agreement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_NetNotionalAmountofInterestRateAgreements" xlink:href="trtn-20241231.xsd#trtn_NetNotionalAmountofInterestRateAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_NetNotionalAmountofInterestRateAgreements" xlink:to="lab_trtn_NetNotionalAmountofInterestRateAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ForeignTable_2dd7bed1-a84d-4d81-a617-757a23607683_terseLabel_en-US" xlink:label="lab_trtn_ForeignTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign [Table]</link:label>
    <link:label id="lab_trtn_ForeignTable_label_en-US" xlink:label="lab_trtn_ForeignTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign [Table]</link:label>
    <link:label id="lab_trtn_ForeignTable_documentation_en-US" xlink:label="lab_trtn_ForeignTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Foreign [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ForeignTable" xlink:href="trtn-20241231.xsd#trtn_ForeignTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ForeignTable" xlink:to="lab_trtn_ForeignTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_1ea8f438-dab0-48d1-a4b3-36f1f7e34731_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, award vesting period</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_exch_XNYS_1e713935-9624-4326-bad1-292c87c3cd79_terseLabel_en-US" xlink:label="lab_exch_XNYS" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NEW YORK STOCK EXCHANGE, INC.</link:label>
    <link:label id="lab_exch_XNYS_label_en-US" xlink:label="lab_exch_XNYS" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW YORK STOCK EXCHANGE, INC. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_exch_XNYS" xlink:href="https://xbrl.sec.gov/exch/2024/exch-2024.xsd#exch_XNYS"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_exch_XNYS" xlink:to="lab_exch_XNYS" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_e1f77add-6a9e-4165-9144-5e9c7a37e47d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, dividends, per share, declared (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_a1444044-36bb-40cf-a2e6-27b39041969a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ForeignLineItems_5d103829-a3ea-41e5-9da0-d6724256c6b4_terseLabel_en-US" xlink:label="lab_trtn_ForeignLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign [Line Items]</link:label>
    <link:label id="lab_trtn_ForeignLineItems_label_en-US" xlink:label="lab_trtn_ForeignLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign [Line Items]</link:label>
    <link:label id="lab_trtn_ForeignLineItems_documentation_en-US" xlink:label="lab_trtn_ForeignLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Foreign [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ForeignLineItems" xlink:href="trtn-20241231.xsd#trtn_ForeignLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ForeignLineItems" xlink:to="lab_trtn_ForeignLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_9c630a08-6b80-48db-9580-3a401465be0b_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_142920be-ad5e-477b-a53d-bfd90a4336d9_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes (refunded) paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock_5eaaf611-48e4-41e8-b6f3-5385d43a2a74_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disclosure of Long Lived Assets Held-for-sale</link:label>
    <link:label id="lab_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disclosure of Long-Lived Assets Held-for-Sale [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock" xlink:to="lab_us-gaap_DisclosureOfLongLivedAssetsHeldForSaleTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_a26bc71b-64d5-4520-b963-052621f21ca8_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_e5ac9248-6a93-4699-b266-12d197adffe5_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax_1ff33f88-bc0c-4418-9d96-82bd0db99f29_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax (benefit) provision on reclassification of (gain) loss on derivative instruments designated as cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_45483473-8dcf-4bf5-a0b7-096a697eb6eb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_af865920-fbfb-4881-ac2c-1cdb419ddd37_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DerivativeImpactDomain_87b60578-1acc-4004-996c-bfedc3a3d0f7_terseLabel_en-US" xlink:label="lab_trtn_DerivativeImpactDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Impact [Domain]</link:label>
    <link:label id="lab_trtn_DerivativeImpactDomain_label_en-US" xlink:label="lab_trtn_DerivativeImpactDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Impact [Domain]</link:label>
    <link:label id="lab_trtn_DerivativeImpactDomain_documentation_en-US" xlink:label="lab_trtn_DerivativeImpactDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Derivative Impact [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DerivativeImpactDomain" xlink:href="trtn-20241231.xsd#trtn_DerivativeImpactDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DerivativeImpactDomain" xlink:to="lab_trtn_DerivativeImpactDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseImpairmentLoss_d69dfa17-0649-4e6c-a627-2481d2adef4f_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Impairment Loss</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseImpairmentLoss" xlink:to="lab_us-gaap_FinanceLeaseImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeMember_33d3d105-00fb-4299-9444-7a697b725c29_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_OtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressesAddressTypeAxis_e57f03e4-3240-4a7a-821a-d51ef56a9812_terseLabel_en-US" xlink:label="lab_dei_EntityAddressesAddressTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Addresses, Address Type [Axis]</link:label>
    <link:label id="lab_dei_EntityAddressesAddressTypeAxis_label_en-US" xlink:label="lab_dei_EntityAddressesAddressTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Addresses, Address Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressesAddressTypeAxis" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressesAddressTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressesAddressTypeAxis" xlink:to="lab_dei_EntityAddressesAddressTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_6848fd4b-b4d2-47e0-8a66-e5415bb1b619_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CancellationOfCommonStockShares_4d7581e9-7a78-401c-9956-af3899f669ff_terseLabel_en-US" xlink:label="lab_trtn_CancellationOfCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock (in shares)</link:label>
    <link:label id="lab_trtn_CancellationOfCommonStockShares_label_en-US" xlink:label="lab_trtn_CancellationOfCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock, Shares</link:label>
    <link:label id="lab_trtn_CancellationOfCommonStockShares_documentation_en-US" xlink:label="lab_trtn_CancellationOfCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CancellationOfCommonStockShares" xlink:href="trtn-20241231.xsd#trtn_CancellationOfCommonStockShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CancellationOfCommonStockShares" xlink:to="lab_trtn_CancellationOfCommonStockShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_b2032b5e-5aaf-4f17-9446-430bba323724_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_d84a6df3-33b4-413b-80a8-15525b03b36f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtAndCapitalLeaseObligations_8a26ba9f-9cb4-4160-b98d-7724df2978bb_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt outstanding</link:label>
    <link:label id="lab_us-gaap_DebtAndCapitalLeaseObligations_85264be0-6032-462a-b097-dd8b1e6e3b43_terseLabel_en-US" xlink:label="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt and lease obligation</link:label>
    <link:label id="lab_us-gaap_DebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_d911210c-8fb5-4750-b582-ca51a2ed005a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, number of shares available for grant</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LeasingMargin_0f2bde75-d481-4dcc-ba3d-a0feae2cad4a_terseLabel_en-US" xlink:label="lab_trtn_LeasingMargin" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing margin</link:label>
    <link:label id="lab_trtn_LeasingMargin_label_en-US" xlink:label="lab_trtn_LeasingMargin" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasing Margin</link:label>
    <link:label id="lab_trtn_LeasingMargin_documentation_en-US" xlink:label="lab_trtn_LeasingMargin" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leasing Margin</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LeasingMargin" xlink:href="trtn-20241231.xsd#trtn_LeasingMargin"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LeasingMargin" xlink:to="lab_trtn_LeasingMargin" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract_2e0c1c9b-b955-48f7-a6ab-3cb62d108403_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized [Abstract]</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CorporateNotesMember_d6e48a51-ba5e-4a6a-9dc5-71a59da06241_terseLabel_en-US" xlink:label="lab_trtn_CorporateNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior notes</link:label>
    <link:label id="lab_trtn_CorporateNotesMember_label_en-US" xlink:label="lab_trtn_CorporateNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Notes [Member]</link:label>
    <link:label id="lab_trtn_CorporateNotesMember_documentation_en-US" xlink:label="lab_trtn_CorporateNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Corporate Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CorporateNotesMember" xlink:href="trtn-20241231.xsd#trtn_CorporateNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CorporateNotesMember" xlink:to="lab_trtn_CorporateNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_121607d8-fcda-4268-a776-9863b9e77d91_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ChassisMember_f72b16a0-5926-4585-992a-d5b7900b51e1_terseLabel_en-US" xlink:label="lab_trtn_ChassisMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chassis</link:label>
    <link:label id="lab_trtn_ChassisMember_label_en-US" xlink:label="lab_trtn_ChassisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chassis [Member]</link:label>
    <link:label id="lab_trtn_ChassisMember_documentation_en-US" xlink:label="lab_trtn_ChassisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents intermodal chassis, which are depreciable revenue earnings assets built specifically for the purpose of transporting intermodal containers domestically.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ChassisMember" xlink:href="trtn-20241231.xsd#trtn_ChassisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ChassisMember" xlink:to="lab_trtn_ChassisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_0e907886-d2c7-4f12-8115-144b1e0c1746_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_afdb6589-ee46-4700-b4c3-a4505b572f55_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S.</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_US"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_US" xlink:to="lab_country_US" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RepairExpense_7cb61ee8-51ce-41c5-a1d6-838f46b4ef26_terseLabel_en-US" xlink:label="lab_trtn_RepairExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repair costs</link:label>
    <link:label id="lab_trtn_RepairExpense_label_en-US" xlink:label="lab_trtn_RepairExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repair Expense</link:label>
    <link:label id="lab_trtn_RepairExpense_documentation_en-US" xlink:label="lab_trtn_RepairExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repair Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RepairExpense" xlink:href="trtn-20241231.xsd#trtn_RepairExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RepairExpense" xlink:to="lab_trtn_RepairExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_729daf9f-4fc9-4bb6-8e93-175cab63b2ca_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing revenues:</link:label>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_c85819d3-357c-4cbc-9a7b-b32c4c3ad0c3_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury share acquired (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockSharesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LeaseFinancePortfolioBenchmarkMember_710e1edd-b71d-4415-aebe-08918a021ebd_terseLabel_en-US" xlink:label="lab_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Finance Portfolio Benchmark</link:label>
    <link:label id="lab_trtn_LeaseFinancePortfolioBenchmarkMember_label_en-US" xlink:label="lab_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Finance Portfolio Benchmark [Member]</link:label>
    <link:label id="lab_trtn_LeaseFinancePortfolioBenchmarkMember_documentation_en-US" xlink:label="lab_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Finance Portfolio Benchmark</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:href="trtn-20241231.xsd#trtn_LeaseFinancePortfolioBenchmarkMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:to="lab_trtn_LeaseFinancePortfolioBenchmarkMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_e6c5bdd8-a86b-446e-8695-01356d7b0da3_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred foreign tax expense</link:label>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Foreign Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredForeignIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_eda663b2-3c8d-4e3c-a1ce-9e3dd28ab6bd_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TritonInternationalLimitedHoldingsMember_8a5f6d2d-8305-42bf-aa3c-6fac0d3e9497_terseLabel_en-US" xlink:label="lab_trtn_TritonInternationalLimitedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Triton International Limited Holdings</link:label>
    <link:label id="lab_trtn_TritonInternationalLimitedHoldingsMember_label_en-US" xlink:label="lab_trtn_TritonInternationalLimitedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Triton International Limited Holdings [Member]</link:label>
    <link:label id="lab_trtn_TritonInternationalLimitedHoldingsMember_documentation_en-US" xlink:label="lab_trtn_TritonInternationalLimitedHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Triton International Limited Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TritonInternationalLimitedHoldingsMember" xlink:href="trtn-20241231.xsd#trtn_TritonInternationalLimitedHoldingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TritonInternationalLimitedHoldingsMember" xlink:to="lab_trtn_TritonInternationalLimitedHoldingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_9597959d-15cd-4cd1-bd7b-ed8871352bed_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EquipmentLeasingMember_bfb372aa-b573-42f9-9d32-de98ebb391ba_terseLabel_en-US" xlink:label="lab_trtn_EquipmentLeasingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment Leasing</link:label>
    <link:label id="lab_trtn_EquipmentLeasingMember_label_en-US" xlink:label="lab_trtn_EquipmentLeasingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Leasing [Member]</link:label>
    <link:label id="lab_trtn_EquipmentLeasingMember_documentation_en-US" xlink:label="lab_trtn_EquipmentLeasingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the equipment leasing segment of the entity which owns, leases and ultimately disposes of containers and chassis from its lease fleet, as well as manages containers owned by third parties.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EquipmentLeasingMember" xlink:href="trtn-20241231.xsd#trtn_EquipmentLeasingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_EquipmentLeasingMember" xlink:to="lab_trtn_EquipmentLeasingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_2893fdc5-c326-4de2-9601-de62778a076e_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, consideration received on transaction</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_f1f47968-e4c7-4662-9220-6c1f9ca1ac12_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury Shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_505fdbd4-1fbd-41ce-94f6-1f49e0adfffa_totalLabel_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income taxes payable</link:label>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_label_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TaxesPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesPayableCurrent" xlink:to="lab_us-gaap_TaxesPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_d2fb7361-8a25-4a23-9e4c-171426d17877_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other operating expenses</link:label>
    <link:label id="lab_us-gaap_OtherCostAndExpenseOperating_label_en-US" xlink:label="lab_us-gaap_OtherCostAndExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Cost and Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCostAndExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherCostAndExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCostAndExpenseOperating" xlink:to="lab_us-gaap_OtherCostAndExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ABSFacilityMember_7e420c4a-d55a-4164-97f1-905cf22eb72e_terseLabel_en-US" xlink:label="lab_trtn_ABSFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ABS Facility</link:label>
    <link:label id="lab_trtn_ABSFacilityMember_label_en-US" xlink:label="lab_trtn_ABSFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ABS Facility [Member]</link:label>
    <link:label id="lab_trtn_ABSFacilityMember_documentation_en-US" xlink:label="lab_trtn_ABSFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">ABS Fixed Rate Series</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ABSFacilityMember" xlink:href="trtn-20241231.xsd#trtn_ABSFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ABSFacilityMember" xlink:to="lab_trtn_ABSFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_b75b0801-82b2-472a-bcf3-5555f4e01477_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_5d012ab0-b0a5-47eb-a8db-e975efcb8d7d_terseLabel_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Doubtful Accounts</link:label>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_c72fc15e-f05f-4285-b365-e45c6f3c1eb8_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned_201b76a6-18d8-47f6-b4b0-19b901f93416_terseLabel_en-US" xlink:label="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collections on finance lease receivables, net of income earned</link:label>
    <link:label id="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned_label_en-US" xlink:label="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Cash Collections on Finance Lease Receivables, Net of Income Earned</link:label>
    <link:label id="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned_documentation_en-US" xlink:label="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Cash Collections on Finance Lease Receivables, Net of Income Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:href="trtn-20241231.xsd#trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:to="lab_trtn_IncreaseDecreaseInCashCollectionsonFinanceLeaseReceivablesNetofIncomeEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_133fde75-9c07-4a86-bf31-e667849d9bda_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_e802f5c1-f063-4ce2-9b9a-67a43e0b5971_totalLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_CostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_89229a73-31b4-4eba-a22c-eae8581036e0_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition, Acquiree [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Acquiree [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_5bcb8037-7b22-4923-9367-6a1d43a24901_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, collateral amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:to="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock_c4f2aad0-e1c3-4155-8334-cd2044bbd3d0_terseLabel_en-US" xlink:label="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration of Credit Risk</link:label>
    <link:label id="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock_label_en-US" xlink:label="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration of Credit Risk [Policy Text Block]</link:label>
    <link:label id="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock_documentation_en-US" xlink:label="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of the accounting policy for any concentrations existing at the date of the financial statements that make an entity vulnerable to a reasonably possible, near-term, severe impact. This disclosure informs financial statement users about the general nature of the risk associated with the concentration, and may indicate the percentage of concentration risk as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:href="trtn-20241231.xsd#trtn_ConcentrationOfCreditRiskPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:to="lab_trtn_ConcentrationOfCreditRiskPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_f1310fe0-bada-4fc7-83b3-4ab5c5360e27_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental non-cash investing activities:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_2e5cfdf9-69b8-4929-a099-72c4553faf36_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_5f35f772-2a2f-461a-9141-8d7741321783_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_FinancingLeaseLeaseIncome_13fc9a5d-7b07-4821-938d-913fb62e30f0_terseLabel_en-US" xlink:label="lab_trtn_FinancingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance leases</link:label>
    <link:label id="lab_trtn_FinancingLeaseLeaseIncome_label_en-US" xlink:label="lab_trtn_FinancingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Lease, Lease Income</link:label>
    <link:label id="lab_trtn_FinancingLeaseLeaseIncome_documentation_en-US" xlink:label="lab_trtn_FinancingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_FinancingLeaseLeaseIncome" xlink:href="trtn-20241231.xsd#trtn_FinancingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_FinancingLeaseLeaseIncome" xlink:to="lab_trtn_FinancingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_42f8a99b-b136-4a67-86ef-e1fc04a5fb6e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_192131e9-b308-4b63-a086-b2230d9b90a3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Share repurchase to settle shareholder tax obligations</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_AllShareConsiderationMember_8e0171b0-aadf-432d-852c-23879bb57008_terseLabel_en-US" xlink:label="lab_trtn_AllShareConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Share Consideration</link:label>
    <link:label id="lab_trtn_AllShareConsiderationMember_label_en-US" xlink:label="lab_trtn_AllShareConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Share Consideration [Member]</link:label>
    <link:label id="lab_trtn_AllShareConsiderationMember_documentation_en-US" xlink:label="lab_trtn_AllShareConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">All Share Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_AllShareConsiderationMember" xlink:href="trtn-20241231.xsd#trtn_AllShareConsiderationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_AllShareConsiderationMember" xlink:to="lab_trtn_AllShareConsiderationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_998d1cbf-2cb0-4314-bb62-9d82681655a5_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock_6eb6a8bf-390c-4fd9-95dc-06e58c515b6c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLeaseIncomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_5d97ae9e-227c-49c0-bd6b-04434c1cc822_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation of Leasing Equipment</link:label>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:to="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets_3c384cfa-a319-4440-9a7b-8566a922abca_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and other intangible amortization</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Goodwill and Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne_61d06c7c-9b15-463e-b7c3-eacdd50d9ad6_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year One</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_705dc88b-d700-4a31-91f3-e077eb1d78c3_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_3ed20fc3-5ec0-4b89-bc4c-2677d00278b4_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Beginning Balance</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_f35f655d-fef4-42fb-b186-3bc2b7c41b4a_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Ending Balance</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_361fa635-329c-452c-8c37-aed49cb6b878_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual Weighted Avg Interest Rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_81b66421-bde8-4ef8-9dde-483a48b3738c_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current foreign tax expense</link:label>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Foreign Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CurrentForeignTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorUnearnedIncome_ed371107-b748-4369-ad6d-89e83155d412_negatedTerseLabel_en-US" xlink:label="lab_trtn_LessorUnearnedIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unearned income</link:label>
    <link:label id="lab_trtn_LessorUnearnedIncome_label_en-US" xlink:label="lab_trtn_LessorUnearnedIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Unearned Income</link:label>
    <link:label id="lab_trtn_LessorUnearnedIncome_documentation_en-US" xlink:label="lab_trtn_LessorUnearnedIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Unearned Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorUnearnedIncome" xlink:href="trtn-20241231.xsd#trtn_LessorUnearnedIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorUnearnedIncome" xlink:to="lab_trtn_LessorUnearnedIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_43b8b68b-4122-4efa-be50-a8da5ecf90a9_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax_c6c0109e-8a9f-4c53-be46-22b1565bd714_terseLabel_en-US" xlink:label="lab_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Translation adjustment functional to reporting currency, increase (decrease), gross of tax</link:label>
    <link:label id="lab_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax_label_en-US" xlink:label="lab_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Translation Adjustment Functional to Reporting Currency, Increase (Decrease), Gross of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax" xlink:to="lab_us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyIncreaseDecreaseGrossOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_3f059d93-aa58-4b53-9a49-e01e6ad61d90_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ImpairmentDomain_05323d4f-d5cc-47c8-b1e3-f2aa86e0e26f_terseLabel_en-US" xlink:label="lab_trtn_ImpairmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment [Domain]</link:label>
    <link:label id="lab_trtn_ImpairmentDomain_label_en-US" xlink:label="lab_trtn_ImpairmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment [Domain]</link:label>
    <link:label id="lab_trtn_ImpairmentDomain_documentation_en-US" xlink:label="lab_trtn_ImpairmentDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Impairment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ImpairmentDomain" xlink:href="trtn-20241231.xsd#trtn_ImpairmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ImpairmentDomain" xlink:to="lab_trtn_ImpairmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_5b2bcbfd-9c22-4e31-b9b0-eafa6a4db524_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowances</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_b4833157-2ddf-410d-a123-5b012f40b5b4_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, redemption price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Redemption Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockRedemptionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:to="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TCFVIIIDistributionMember_ebdce8d8-7072-43dc-96a9-f69b5e63099f_terseLabel_en-US" xlink:label="lab_trtn_TCFVIIIDistributionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TCF VIII Distribution</link:label>
    <link:label id="lab_trtn_TCFVIIIDistributionMember_label_en-US" xlink:label="lab_trtn_TCFVIIIDistributionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TCF VIII Distribution [Member]</link:label>
    <link:label id="lab_trtn_TCFVIIIDistributionMember_documentation_en-US" xlink:label="lab_trtn_TCFVIIIDistributionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">TCF VIII Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TCFVIIIDistributionMember" xlink:href="trtn-20241231.xsd#trtn_TCFVIIIDistributionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TCFVIIIDistributionMember" xlink:to="lab_trtn_TCFVIIIDistributionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts_da7337d0-0d05-4c1a-9341-b42bda59f4df_terseLabel_en-US" xlink:label="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, net of unamortized costs of $48,743 and $43,924</link:label>
    <link:label id="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts_e403b1de-fe35-4ea9-9e1e-21de6d4e573d_totalLabel_en-US" xlink:label="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Debt, net of unamortized costs</link:label>
    <link:label id="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts_label_en-US" xlink:label="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Capital Lease Obligations, net of deferred financing costs</link:label>
    <link:label id="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts_documentation_en-US" xlink:label="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt and Capital Lease Obligations, net of deferred financing costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:href="trtn-20241231.xsd#trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:to="lab_trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears_e7a85252-2b4d-46cd-a6d4-b599713c11b0_verboseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TermNotesMember_731339b6-1e26-4d44-9723-028efd336a70_terseLabel_en-US" xlink:label="lab_trtn_TermNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term loan tranche</link:label>
    <link:label id="lab_trtn_TermNotesMember_label_en-US" xlink:label="lab_trtn_TermNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Notes [Member]</link:label>
    <link:label id="lab_trtn_TermNotesMember_documentation_en-US" xlink:label="lab_trtn_TermNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TermNotesMember" xlink:href="trtn-20241231.xsd#trtn_TermNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TermNotesMember" xlink:to="lab_trtn_TermNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_868c0537-6a4e-41d6-a876-194f5b562db4_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_6a87e2c7-48f1-471e-9254-f0d4204b89f4_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent_be17b745-d485-4de2-8315-83c26e725379_terseLabel_en-US" xlink:label="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment tax credit, federal taxable income offset, percent</link:label>
    <link:label id="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent_label_en-US" xlink:label="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Federal Taxable Income Offset, Percent</link:label>
    <link:label id="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent_documentation_en-US" xlink:label="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Federal Taxable Income Offset, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:href="trtn-20241231.xsd#trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:to="lab_trtn_InvestmentTaxCreditFederalTaxableIncomeOffsetPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_9975c512-6800-485f-8910-cf5ea1a02ac2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_a911eea5-2c6e-4e41-87e2-6fdca238cb74_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_f5ec140f-2341-4e72-a439-15e11b2dd6b9_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common shares to Parent</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payments for) Other Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentRegistrationStatement_5ff8090d-93db-4d19-b1d4-bb6c4525189f_terseLabel_en-US" xlink:label="lab_dei_DocumentRegistrationStatement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Registration Statement</link:label>
    <link:label id="lab_dei_DocumentRegistrationStatement_label_en-US" xlink:label="lab_dei_DocumentRegistrationStatement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Registration Statement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentRegistrationStatement" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentRegistrationStatement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentRegistrationStatement" xlink:to="lab_dei_DocumentRegistrationStatement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_a6301672-f264-449a-b17c-8c29026ca7e9_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TankContainerUnitsMember_c4d79fc1-e69a-4f55-9228-4436eaf44494_terseLabel_en-US" xlink:label="lab_trtn_TankContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tank container</link:label>
    <link:label id="lab_trtn_TankContainerUnitsMember_label_en-US" xlink:label="lab_trtn_TankContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tank Container Units [Member]</link:label>
    <link:label id="lab_trtn_TankContainerUnitsMember_documentation_en-US" xlink:label="lab_trtn_TankContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents tank containers, which are depreciable revenue earnings assets used to carry bulk liquids such as chemicals.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TankContainerUnitsMember" xlink:href="trtn-20241231.xsd#trtn_TankContainerUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TankContainerUnitsMember" xlink:to="lab_trtn_TankContainerUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CustomerTwoMember_baf2226b-49ab-490a-a569-b655a4557e72_terseLabel_en-US" xlink:label="lab_trtn_CustomerTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Two</link:label>
    <link:label id="lab_trtn_CustomerTwoMember_label_en-US" xlink:label="lab_trtn_CustomerTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Two [Member]</link:label>
    <link:label id="lab_trtn_CustomerTwoMember_documentation_en-US" xlink:label="lab_trtn_CustomerTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CustomerTwoMember" xlink:href="trtn-20241231.xsd#trtn_CustomerTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CustomerTwoMember" xlink:to="lab_trtn_CustomerTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_34ed804b-8216-42d3-a862-ebdac4f0294d_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_f7b3ef53-0475-444e-93db-c6c7fae16cd9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, basis spread on variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_ContactPersonnelEmailAddress_462e5c5b-fc3c-4933-a149-ea6d604b6956_terseLabel_en-US" xlink:label="lab_dei_ContactPersonnelEmailAddress" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contact Personnel Email Address</link:label>
    <link:label id="lab_dei_ContactPersonnelEmailAddress_label_en-US" xlink:label="lab_dei_ContactPersonnelEmailAddress" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contact Personnel Email Address</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_ContactPersonnelEmailAddress" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_ContactPersonnelEmailAddress"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_ContactPersonnelEmailAddress" xlink:to="lab_dei_ContactPersonnelEmailAddress" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo_d942fbcd-296b-48a2-b9e2-9326aa3e9173_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Two</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_63b156f0-18f4-4a9c-b65f-e02e82930c14_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_55812802-0c68-469d-9eb4-d9dba7aef492_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_549acfe6-e47d-4251-8abf-50d15c1734b9_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net deferred income tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilities" xlink:to="lab_us-gaap_DeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock_60fcc647-1de5-441c-997a-0423e4da3960_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic allocation of revenues for the periods indicated based on the customers primary domicile and allocates equipment trading revenue based on the location of sale</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Revenue from External Customers and Long-Lived Assets, by Geographical Areas [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_7eb83417-17d9-4b2c-b2e2-d9599f13e513_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock_1add1e45-4164-4633-ba86-c33f4d434640_terseLabel_en-US" xlink:label="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing Equipment</link:label>
    <link:label id="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock_label_en-US" xlink:label="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Subject to or Available for Operating Lease Net [Policy Text Block]</link:label>
    <link:label id="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock_documentation_en-US" xlink:label="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of accounting policy for property subject to or available for operating lease.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:href="trtn-20241231.xsd#trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:to="lab_trtn_PropertySubjectToOrAvailableForOperatingLeaseNetPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost_6fde7b8e-5180-4f6d-92b0-fee7b25566a0_terseLabel_en-US" xlink:label="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt termination expense</link:label>
    <link:label id="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost_label_en-US" xlink:label="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Debt Issuance Cost, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WriteOffOfDeferredDebtIssuanceCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:to="lab_us-gaap_WriteOffOfDeferredDebtIssuanceCost" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_e9c92e87-0cd5-435d-b527-1df72cdfebbe_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_IcfrAuditorAttestationFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_IcfrAuditorAttestationFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_IcfrAuditorAttestationFlag" xlink:to="lab_dei_IcfrAuditorAttestationFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_312b8891-7a26-4146-86aa-1a117a6435fd_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_e6b9a617-89bd-4531-9475-d46e28115e3d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_ac1a56cf-f208-4fd7-991b-011117900f70_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_f11f9cdf-2698-42c0-820f-695c95be22b1_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency Translation and Re-measurement</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_17d58694-82b7-4161-9ad2-d284fcd0ef45_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_a98d8095-ca8a-4da0-815b-36ac6ac83b48_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net (gain) loss on sale of leasing equipment</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnSaleOfProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfProperties" xlink:to="lab_us-gaap_GainLossOnSaleOfProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_519a58b7-edc0-4fb0-965c-66d6c9156b8e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_0dca13f1-853d-48b3-be6b-835fd668b633_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Value</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockLiquidationPreferenceValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:to="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_f4c80428-7dbd-4427-a9a7-99f6f4012724_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_d51885f7-cefc-4dc3-b72f-0fbe7d79fd37_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_d9b888c6-9369-4a46-876c-6d0f8ca68fd4_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk, percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_e28dbb74-6293-404a-b774-2ee5af7054ab_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_98591bda-4cb5-4f93-8d38-0de3b61b9272_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss and interest expense limitation carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears_555f7ed1-ceab-4896-9b19-0864050be176_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare_fc35c686-2976-40f7-8b84-b63a6906dfb8_terseLabel_en-US" xlink:label="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash consideration per acquiree share (in usd per share)</link:label>
    <link:label id="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare_label_en-US" xlink:label="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Cash Consideration Per Acquiree Share</link:label>
    <link:label id="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare_documentation_en-US" xlink:label="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Cash Consideration Per Acquiree Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:href="trtn-20241231.xsd#trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:to="lab_trtn_BusinessCombinationConsiderationTransferredCashConsiderationPerAcquireeShare" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_FixedRateDebtMember_e7d7c8a5-1f21-4e97-ab85-3c638fe1327f_terseLabel_en-US" xlink:label="lab_trtn_FixedRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Rate Debt</link:label>
    <link:label id="lab_trtn_FixedRateDebtMember_label_en-US" xlink:label="lab_trtn_FixedRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate Debt [Member]</link:label>
    <link:label id="lab_trtn_FixedRateDebtMember_documentation_en-US" xlink:label="lab_trtn_FixedRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Rate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_FixedRateDebtMember" xlink:href="trtn-20241231.xsd#trtn_FixedRateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_FixedRateDebtMember" xlink:to="lab_trtn_FixedRateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_5ca9b8c4-2e96-421f-9888-49dfe4493834_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of derivative instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations_71a603c0-ff3b-4efe-a465-6f8bb4a1d06d_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payments under debt facilities and finance lease obligations</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_RepaymentsOfDebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ReturnOfCapitalToParent_06eb92c8-927e-474e-bfd7-6d61fe650c49_negatedTerseLabel_en-US" xlink:label="lab_trtn_ReturnOfCapitalToParent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Return of capital to Parent</link:label>
    <link:label id="lab_trtn_ReturnOfCapitalToParent_label_en-US" xlink:label="lab_trtn_ReturnOfCapitalToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Return of Capital to Parent</link:label>
    <link:label id="lab_trtn_ReturnOfCapitalToParent_documentation_en-US" xlink:label="lab_trtn_ReturnOfCapitalToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Return of Capital to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ReturnOfCapitalToParent" xlink:href="trtn-20241231.xsd#trtn_ReturnOfCapitalToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ReturnOfCapitalToParent" xlink:to="lab_trtn_ReturnOfCapitalToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_71c37d29-2d36-4e56-a88b-3c4541ca7b5a_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorFutureMinimumLeasePaymentReceivable_d8dee058-ebd2-4591-a517-eb6388c42667_terseLabel_en-US" xlink:label="lab_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future minimum lease payment receivable</link:label>
    <link:label id="lab_trtn_LessorFutureMinimumLeasePaymentReceivable_label_en-US" xlink:label="lab_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Future Minimum Lease Payment Receivable</link:label>
    <link:label id="lab_trtn_LessorFutureMinimumLeasePaymentReceivable_documentation_en-US" xlink:label="lab_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Future Minimum Lease Payment Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:href="trtn-20241231.xsd#trtn_LessorFutureMinimumLeasePaymentReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:to="lab_trtn_LessorFutureMinimumLeasePaymentReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNet_af2232d2-209c-4641-be1d-50a6d915a02d_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net of allowances of $1,317 and $738</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax_a76a20fe-6754-4d8b-858c-eab25cbd98ed_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (gains) losses</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AsiaMember_f4c74ab5-7ab9-4f39-a644-7e18ecff0ffc_terseLabel_en-US" xlink:label="lab_srt_AsiaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asia</link:label>
    <link:label id="lab_srt_AsiaMember_label_en-US" xlink:label="lab_srt_AsiaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asia [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AsiaMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_AsiaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AsiaMember" xlink:to="lab_srt_AsiaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LeasesBillingMember_d73d6861-22df-4c38-8f85-31b41b2c00c5_terseLabel_en-US" xlink:label="lab_trtn_LeasesBillingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases Billing</link:label>
    <link:label id="lab_trtn_LeasesBillingMember_label_en-US" xlink:label="lab_trtn_LeasesBillingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases Billing [Member]</link:label>
    <link:label id="lab_trtn_LeasesBillingMember_documentation_en-US" xlink:label="lab_trtn_LeasesBillingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leases Billing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LeasesBillingMember" xlink:href="trtn-20241231.xsd#trtn_LeasesBillingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LeasesBillingMember" xlink:to="lab_trtn_LeasesBillingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_80825867-270c-4ac5-aefb-af340863bb91_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_4c3798e0-fdd7-43d9-88cb-3f38ba1b8a32_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LossGainAxis_11afe734-4718-4a68-8ef7-9e51f1c9acc6_terseLabel_en-US" xlink:label="lab_trtn_LossGainAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Loss) gain [Axis]</link:label>
    <link:label id="lab_trtn_LossGainAxis_label_en-US" xlink:label="lab_trtn_LossGainAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">(Loss) gain [Axis]</link:label>
    <link:label id="lab_trtn_LossGainAxis_documentation_en-US" xlink:label="lab_trtn_LossGainAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">(Loss) gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LossGainAxis" xlink:href="trtn-20241231.xsd#trtn_LossGainAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LossGainAxis" xlink:to="lab_trtn_LossGainAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_c79ffb6e-4707-4f1e-b376-df396ef91c3d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EuropeMember_331f3212-41cd-42b5-8900-17c6c88dd2bc_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Europe</link:label>
    <link:label id="lab_srt_EuropeMember_label_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Europe [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EuropeMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EuropeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EuropeMember" xlink:to="lab_srt_EuropeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorGrossFinancingLeaseReceivables_7a005daa-f1df-4996-aa38-4e33cf1ea58d_totalLabel_en-US" xlink:label="lab_trtn_LessorGrossFinancingLeaseReceivables" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross finance lease receivable</link:label>
    <link:label id="lab_trtn_LessorGrossFinancingLeaseReceivables_label_en-US" xlink:label="lab_trtn_LessorGrossFinancingLeaseReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Gross Financing lease Receivables.</link:label>
    <link:label id="lab_trtn_LessorGrossFinancingLeaseReceivables_documentation_en-US" xlink:label="lab_trtn_LessorGrossFinancingLeaseReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of remaining payments as of the balance sheet date that lessees are obligated to make or can be required to make under direct financing and sales-type leases, net of allowance for uncollectible minimum lease payments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorGrossFinancingLeaseReceivables" xlink:href="trtn-20241231.xsd#trtn_LessorGrossFinancingLeaseReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorGrossFinancingLeaseReceivables" xlink:to="lab_trtn_LessorGrossFinancingLeaseReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_cbc7f7d6-8346-4ae9-8888-e385b771ede8_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment_9eb032e6-fb7b-41b0-93a3-acfb608bfb25_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Effect of investment tax credit purchase</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Investment, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment_6bdfd241-4792-4f70-b534-604ee190b7b9_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Effective income tax rate reconciliation, tax credit, investment, amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Investment, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxReconciliationTaxCreditsInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment" xlink:to="lab_us-gaap_IncomeTaxReconciliationTaxCreditsInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_OtherInternationalCountriesMember_9e7fd308-f845-4498-8a75-5df4343d9832_terseLabel_en-US" xlink:label="lab_trtn_OtherInternationalCountriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other International</link:label>
    <link:label id="lab_trtn_OtherInternationalCountriesMember_label_en-US" xlink:label="lab_trtn_OtherInternationalCountriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other International Countries [Member]</link:label>
    <link:label id="lab_trtn_OtherInternationalCountriesMember_documentation_en-US" xlink:label="lab_trtn_OtherInternationalCountriesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the geographic area of international countries other than Asia and Europe.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_OtherInternationalCountriesMember" xlink:href="trtn-20241231.xsd#trtn_OtherInternationalCountriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_OtherInternationalCountriesMember" xlink:to="lab_trtn_OtherInternationalCountriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_e8806597-b6eb-4e12-b7cb-6b35a901a27b_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases receivable, related parties</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_2c17c66b-4a3c-4226-9226-7b4d16f4f3a9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), net of tax:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease_bc763a96-363c-492e-a1de-6b3d020d7b46_terseLabel_en-US" xlink:label="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, equipment lease, increase (decrease)</link:label>
    <link:label id="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease_label_en-US" xlink:label="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Equipment Lease, Increase (Decrease)</link:label>
    <link:label id="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease_documentation_en-US" xlink:label="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Expense, Equipment Lease, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:href="trtn-20241231.xsd#trtn_InterestExpenseEquipmentLeaseIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:to="lab_trtn_InterestExpenseEquipmentLeaseIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_5b96e627-9aab-414e-a7f4-64607546a8df_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_a430da60-6f53-42f8-a9ca-76cfad6e629d_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total shareholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_c5e26500-db01-40cb-be6b-986bf36226af_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsGross" xlink:to="lab_us-gaap_DeferredTaxAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_ContactPersonnelName_855b8879-e7aa-471a-9434-5b5d01676f42_terseLabel_en-US" xlink:label="lab_dei_ContactPersonnelName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contact Personnel Name</link:label>
    <link:label id="lab_dei_ContactPersonnelName_label_en-US" xlink:label="lab_dei_ContactPersonnelName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contact Personnel Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_ContactPersonnelName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_ContactPersonnelName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_ContactPersonnelName" xlink:to="lab_dei_ContactPersonnelName" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityVoluntaryFilers_99c7ba4e-7cb9-403c-b3d0-1a8e94eba6d4_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_AssetBackedSecuritizationTermNotesMember_cabafc19-e712-423b-a62a-605e745cf0e3_terseLabel_en-US" xlink:label="lab_trtn_AssetBackedSecuritizationTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed securitization term notes</link:label>
    <link:label id="lab_trtn_AssetBackedSecuritizationTermNotesMember_label_en-US" xlink:label="lab_trtn_AssetBackedSecuritizationTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Backed Securitization Term Notes [Member]</link:label>
    <link:label id="lab_trtn_AssetBackedSecuritizationTermNotesMember_documentation_en-US" xlink:label="lab_trtn_AssetBackedSecuritizationTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents term notes which are collateralized by a specific group of underlying assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_AssetBackedSecuritizationTermNotesMember" xlink:href="trtn-20241231.xsd#trtn_AssetBackedSecuritizationTermNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_AssetBackedSecuritizationTermNotesMember" xlink:to="lab_trtn_AssetBackedSecuritizationTermNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_14c10b7c-16c3-4ed6-91c3-f9661b7e392c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_eae3c23c-5df4-4ad3-836b-23f6a3b78dce_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combinations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsAbstract" xlink:to="lab_us-gaap_BusinessCombinationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_cabaa125-be0b-49e9-bb7f-2e0b31e48939_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_6e5c9779-80d7-405f-a848-7688ac1b175e_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_e487600e-9ca2-458b-b9cc-f508a3f254b4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and debt expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpenseNonoperating"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_38ac2a06-bd9f-495c-83d5-732e99492662_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income taxes</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_2dbc8f42-b2e7-4a18-ba37-8f032dcb3048_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares_0bd278c8-39eb-4424-81c2-774742e9e59e_totalLabel_en-US" xlink:label="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income attributable to common shareholder</link:label>
    <link:label id="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares_label_en-US" xlink:label="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent Including Dividends on Preferred Shares</link:label>
    <link:label id="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares_documentation_en-US" xlink:label="lab_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent Including Dividends on Preferred Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares" xlink:href="trtn-20241231.xsd#trtn_ComprehensiveIncomeLossNetofTaxAttributabletoParentIncludingDividendsonPreferredShares"/>
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    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_05b709ce-c6d6-491e-b774-f7b593478548_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of credit outstanding , amount</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCountry_c7b4f6d7-f90d-4fb9-952d-66a6334d0799_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:label id="lab_dei_EntityAddressCountry_label_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressCountry"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_c609c215-5fb1-4e7d-af36-a1a8a77eed05_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined contribution plan, cost</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:to="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter_b4f1e27e-917f-43f7-b829-a5d1eea8496a_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorFinanceLeaseReserve_fc3175c8-3e89-4ab0-99e5-6b0bff0948cf_negatedTerseLabel_en-US" xlink:label="lab_trtn_LessorFinanceLeaseReserve" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Lessor, Finance Lease Reserve</link:label>
    <link:label id="lab_trtn_LessorFinanceLeaseReserve_label_en-US" xlink:label="lab_trtn_LessorFinanceLeaseReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Finance Lease Reserve</link:label>
    <link:label id="lab_trtn_LessorFinanceLeaseReserve_documentation_en-US" xlink:label="lab_trtn_LessorFinanceLeaseReserve" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Finance Lease Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorFinanceLeaseReserve" xlink:href="trtn-20241231.xsd#trtn_LessorFinanceLeaseReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorFinanceLeaseReserve" xlink:to="lab_trtn_LessorFinanceLeaseReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCapMember_04b3b129-2ac8-439e-99cd-18eba61a96e1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Cap</link:label>
    <link:label id="lab_us-gaap_InterestRateCapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Cap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestRateCapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCapMember" xlink:to="lab_us-gaap_InterestRateCapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt_401ae232-92f6-46d0-8425-30ed71cf803e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from related party</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Repayments of) Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt" xlink:to="lab_us-gaap_ProceedsFromRepaymentsOfRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExaminationInterestAccrued_68911d5e-3e78-4dd2-b2d5-5be61933bbae_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationInterestAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest accrued</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExaminationInterestAccrued_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationInterestAccrued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Examination, Interest Accrued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExaminationInterestAccrued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExaminationInterestAccrued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExaminationInterestAccrued" xlink:to="lab_us-gaap_IncomeTaxExaminationInterestAccrued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_40e79f1d-d871-4946-ad73-8c6662c79091_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsHeldForSaleNotPartOfDisposalGroupCurrent_b883e129-ade1-4d1e-82a5-e2bf40ec748c_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsHeldForSaleNotPartOfDisposalGroupCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsHeldForSaleNotPartOfDisposalGroupCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsHeldForSaleNotPartOfDisposalGroupCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset, Held-for-Sale, Not Part of Disposal Group, Current</link:label>
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    <link:label id="lab_us-gaap_LongTermDebt_b5545cfb-aa19-40ec-ab83-c2756384b823_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total debt outstanding</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_301236ef-ae7e-4119-8a68-d30cc1039026_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_009fb982-eb3c-452a-a3cf-bc269e70e7e6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax (benefit) provision on change in derivative instruments designated as cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax"/>
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    <link:label id="lab_trtn_AdjustmentsToAdditionalPaidInCapitalContributedCapitalFromParent_dde0c408-ddc2-4ba2-83e2-91dea78e3f47_terseLabel_en-US" xlink:label="lab_trtn_AdjustmentsToAdditionalPaidInCapitalContributedCapitalFromParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributed capital from Parent for executive compensation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_trtn_AdjustmentsToAdditionalPaidInCapitalContributedCapitalFromParent" xlink:href="trtn-20241231.xsd#trtn_AdjustmentsToAdditionalPaidInCapitalContributedCapitalFromParent"/>
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    <link:label id="lab_dei_DocumentFiscalPeriodFocus_93ea9d18-4a14-47a0-8e43-4839d41429de_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
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    <link:label id="lab_dei_ExchangeDomain_4cb09cde-ab5b-4e88-9f73-843010b1d157_terseLabel_en-US" xlink:label="lab_dei_ExchangeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange [Domain]</link:label>
    <link:label id="lab_dei_ExchangeDomain_label_en-US" xlink:label="lab_dei_ExchangeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exchange [Domain]</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued_425bad0d-57e1-4440-98d4-6b87b5e34bb7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Penalties</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Examination, Penalties Accrued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExaminationPenaltiesAccrued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExaminationPenaltiesAccrued"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_712cd23d-a42f-45b4-aec6-f774e734815b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_a119784d-0ac6-415f-9de3-53407909a225_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction and other costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_a1c91cfa-1a74-45fe-a325-12ff616f375d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transaction and other costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_82bd2b3e-b791-4aa1-a366-81475e2b74c7_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_7566c600-6177-4ebe-97db-71df47c9a6e9_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined contribution plan, employer matching contribution, percent of match</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Employer Matching Contribution, Percent of Match</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_341d3f9a-3897-4214-af1f-fd6fb763fedc_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ExcludingImpactMember_4f286111-10c2-49c8-85d8-9f4294ffae19_terseLabel_en-US" xlink:label="lab_trtn_ExcludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excluding Impact</link:label>
    <link:label id="lab_trtn_ExcludingImpactMember_label_en-US" xlink:label="lab_trtn_ExcludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excluding Impact [Member]</link:label>
    <link:label id="lab_trtn_ExcludingImpactMember_documentation_en-US" xlink:label="lab_trtn_ExcludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Excluding Impact [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ExcludingImpactMember" xlink:href="trtn-20241231.xsd#trtn_ExcludingImpactMember"/>
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    <link:label id="lab_trtn_EffectiveTaxRateLineItems_45031741-a7b7-4b5c-8fcb-a4b90764ff6b_terseLabel_en-US" xlink:label="lab_trtn_EffectiveTaxRateLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Tax Rate [Line Items]</link:label>
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    <link:label id="lab_trtn_EffectiveTaxRateLineItems_documentation_en-US" xlink:label="lab_trtn_EffectiveTaxRateLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Effective Tax Rate [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EffectiveTaxRateLineItems" xlink:href="trtn-20241231.xsd#trtn_EffectiveTaxRateLineItems"/>
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    <link:label id="lab_us-gaap_MergersAcquisitionsAndDispositionsDisclosuresTextBlock_caa93458-5609-4d1e-a5ae-2fa25f3be7d9_terseLabel_en-US" xlink:label="lab_us-gaap_MergersAcquisitionsAndDispositionsDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Merger</link:label>
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    <link:label id="lab_us-gaap_AssetsAbstract_c68dea7c-75e7-4a26-8aeb-6793da383eaf_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS:</link:label>
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    <link:label id="lab_trtn_SpecialContainerUnitsMember_a8b56fe9-d0f1-4ceb-ac06-cb863d1330e7_terseLabel_en-US" xlink:label="lab_trtn_SpecialContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special container</link:label>
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    <link:label id="lab_trtn_SpecialContainerUnitsMember_documentation_en-US" xlink:label="lab_trtn_SpecialContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents mainly open top and flat rack containers, which are depreciable revenue earnings assets generally used to carry heavy or bulky cargos, such as marble slabs, steel coils, or factory components.</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_bfa367b2-aedd-4517-a5d4-8253339885ab_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
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    <link:label id="lab_dei_DocumentType_ed29dd3b-34af-47b8-90b7-1b7655ad26be_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_9570230e-ce24-4a83-8120-f622a59e7663_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract Type [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_f8aa91fd-fb54-4e34-9a5a-70c17078e501_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual Weighted Avg Interest Rate</link:label>
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    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_3fca21ab-ff85-413f-95ec-50b8f8815846_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (gain) loss on derivative instruments</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_ab7f7ad3-52b1-4452-b6eb-972e6afac923_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of segment information</link:label>
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    <link:label id="lab_us-gaap_LeasesOperatingAbstract_385a61b3-e371-4e96-83bb-16de8af4b0f5_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases, Operating [Abstract]</link:label>
    <link:label id="lab_us-gaap_LeasesOperatingAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases, Operating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesOperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeasesOperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesOperatingAbstract" xlink:to="lab_us-gaap_LeasesOperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock_859b820e-0eae-4835-89c1-b986711c9883_terseLabel_en-US" xlink:label="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Weighted-Average Operating Lease</link:label>
    <link:label id="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock_label_en-US" xlink:label="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Weighted-Average Operating Lease [Table Text Block]</link:label>
    <link:label id="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock_documentation_en-US" xlink:label="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Weighted-Average Operating Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:href="trtn-20241231.xsd#trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:to="lab_trtn_ScheduleOfWeightedAverageOperatingLeaseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_8aef1890-93ec-4525-88a7-5e3e4c834ce3_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ProceedsFromSaleOfBuildingsNet_cbaba98f-ffc1-4073-924c-797f79e2ca3e_terseLabel_en-US" xlink:label="lab_trtn_ProceedsFromSaleOfBuildingsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of equipment, net of selling costs</link:label>
    <link:label id="lab_trtn_ProceedsFromSaleOfBuildingsNet_label_en-US" xlink:label="lab_trtn_ProceedsFromSaleOfBuildingsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Buildings, Net</link:label>
    <link:label id="lab_trtn_ProceedsFromSaleOfBuildingsNet_documentation_en-US" xlink:label="lab_trtn_ProceedsFromSaleOfBuildingsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Buildings, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ProceedsFromSaleOfBuildingsNet" xlink:href="trtn-20241231.xsd#trtn_ProceedsFromSaleOfBuildingsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ProceedsFromSaleOfBuildingsNet" xlink:to="lab_trtn_ProceedsFromSaleOfBuildingsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLocationDomain_c52b1621-0340-4cf0-8c45-e394160d6e91_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Location [Domain]</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLocationDomain_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLocationDomain" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_24f5933b-0d3d-44a4-8b9b-5e83535d8146_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:to="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized_914b0c33-56a1-455d-84eb-929d6419f4fa_totalLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_f590246d-7ccf-435a-b721-85701efe9867_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of deferred revenue</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice_6e3202da-56e9-451d-929e-be45d6215229_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying market price per share (in dollar per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_acb99044-f01a-4492-b24c-d955503db61f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risk-free rate</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RestrictedCashAccountsAxis_81a625be-8afd-4284-885a-123908938b2f_terseLabel_en-US" xlink:label="lab_trtn_RestrictedCashAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RestrictedCashAccounts [Axis]</link:label>
    <link:label id="lab_trtn_RestrictedCashAccountsAxis_label_en-US" xlink:label="lab_trtn_RestrictedCashAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">RestrictedCashAccounts [Axis]</link:label>
    <link:label id="lab_trtn_RestrictedCashAccountsAxis_documentation_en-US" xlink:label="lab_trtn_RestrictedCashAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">RestrictedCashAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RestrictedCashAccountsAxis" xlink:href="trtn-20241231.xsd#trtn_RestrictedCashAccountsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RestrictedCashAccountsAxis" xlink:to="lab_trtn_RestrictedCashAccountsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableAmountPerShare_bf411aac-a779-4e82-bfec-eb60339b75cf_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableAmountPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend approved and declared (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_DividendsPayableAmountPerShare_label_en-US" xlink:label="lab_us-gaap_DividendsPayableAmountPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable, Amount Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableAmountPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPayableAmountPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableAmountPerShare" xlink:to="lab_us-gaap_DividendsPayableAmountPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_7022bac8-b22b-4876-9f1f-61ea49242a90_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RefrigeratedContainerUnitsMember_09f5f678-1905-4f63-a5fc-66a25dc5b7a4_terseLabel_en-US" xlink:label="lab_trtn_RefrigeratedContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Refrigerated container</link:label>
    <link:label id="lab_trtn_RefrigeratedContainerUnitsMember_label_en-US" xlink:label="lab_trtn_RefrigeratedContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Refrigerated Container Units [Member]</link:label>
    <link:label id="lab_trtn_RefrigeratedContainerUnitsMember_documentation_en-US" xlink:label="lab_trtn_RefrigeratedContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents refrigerated containers, which are depreciable revenue earnings assets typically used to carry perishable cargo such as fresh and frozen produce.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RefrigeratedContainerUnitsMember" xlink:href="trtn-20241231.xsd#trtn_RefrigeratedContainerUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RefrigeratedContainerUnitsMember" xlink:to="lab_trtn_RefrigeratedContainerUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_4905c5c0-f59a-44c5-9214-d2bd68a59211_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_0aa49bf0-b247-4939-9e1f-233e215ac33e_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease related amortization</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_4f2b13e4-0848-4a5b-a8bd-cc2aed9dedb6_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_324eb7a0-01fd-4345-b2b1-51199282b719_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Financing Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfFinancingCosts" xlink:to="lab_us-gaap_PaymentsOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_IncludingImpactMember_6ffa6b3e-8f1e-48bd-8cef-efc3ccd5c90d_terseLabel_en-US" xlink:label="lab_trtn_IncludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Including Impact</link:label>
    <link:label id="lab_trtn_IncludingImpactMember_label_en-US" xlink:label="lab_trtn_IncludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Including Impact [Member]</link:label>
    <link:label id="lab_trtn_IncludingImpactMember_documentation_en-US" xlink:label="lab_trtn_IncludingImpactMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Including Impact [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_IncludingImpactMember" xlink:href="trtn-20241231.xsd#trtn_IncludingImpactMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_IncludingImpactMember" xlink:to="lab_trtn_IncludingImpactMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_3a9f22a2-b8f9-4140-adad-e945181feeb2_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_ffca6085-8fc2-42e1-8728-cd0573edb3c7_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues:</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_dc93a720-f476-42aa-bb68-38c01572b46a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_d381c98a-e81b-4329-8d7e-e2aa7b90be6a_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_7e2e5678-0f90-4e3e-9979-eff166c667d9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_StorageAndHandlingExpense_a0d793a2-d9a3-4ca3-8fb3-a3df3864f697_terseLabel_en-US" xlink:label="lab_trtn_StorageAndHandlingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Storage and handling</link:label>
    <link:label id="lab_trtn_StorageAndHandlingExpense_label_en-US" xlink:label="lab_trtn_StorageAndHandlingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Storage and Handling Expense</link:label>
    <link:label id="lab_trtn_StorageAndHandlingExpense_documentation_en-US" xlink:label="lab_trtn_StorageAndHandlingExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Storage and Handling Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_StorageAndHandlingExpense" xlink:href="trtn-20241231.xsd#trtn_StorageAndHandlingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_StorageAndHandlingExpense" xlink:to="lab_trtn_StorageAndHandlingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_daa16203-f3ad-49c0-81bf-a0686a401de4_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorEstimatedResidualReceivable_cccbe41e-ec07-4e5a-b7f2-f5e9cb950fe0_terseLabel_en-US" xlink:label="lab_trtn_LessorEstimatedResidualReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated residual receivable</link:label>
    <link:label id="lab_trtn_LessorEstimatedResidualReceivable_label_en-US" xlink:label="lab_trtn_LessorEstimatedResidualReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Estimated Residual Receivable</link:label>
    <link:label id="lab_trtn_LessorEstimatedResidualReceivable_documentation_en-US" xlink:label="lab_trtn_LessorEstimatedResidualReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Estimated Residual Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorEstimatedResidualReceivable" xlink:href="trtn-20241231.xsd#trtn_LessorEstimatedResidualReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorEstimatedResidualReceivable" xlink:to="lab_trtn_LessorEstimatedResidualReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares_d5221aab-3486-4199-8055-d70484fb607e_terseLabel_en-US" xlink:label="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation (in shares)</link:label>
    <link:label id="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares_label_en-US" xlink:label="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Share-based Compensation, Requisite Service Period Recognition, Shares</link:label>
    <link:label id="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares_documentation_en-US" xlink:label="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Share-based Compensation, Requisite Service Period Recognition, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:href="trtn-20241231.xsd#trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:to="lab_trtn_AdjustmentstoAdditionalPaidinCapitalSharebasedCompensationRequisiteServicePeriodRecognitionShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_e19bd677-48a4-4cf8-bec6-f362780911a2_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing equipment, accumulated depreciation and allowances</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_7adaa7c0-c276-46ae-98a1-3a2b08739f16_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_11584f4a-b1a1-4148-aab4-81ba7b5e9620_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_8f28bf64-fafd-424d-a077-5b2e46f53c2b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_878b05ee-0f76-4648-b9dc-8f0fe85f8a4d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accelerated depreciation</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_e6727afc-d00c-471f-bd3f-d0c3324549dc_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CustomerOneMember_7c5d9002-ba3f-4b96-871c-df7858bea5e5_terseLabel_en-US" xlink:label="lab_trtn_CustomerOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer One</link:label>
    <link:label id="lab_trtn_CustomerOneMember_label_en-US" xlink:label="lab_trtn_CustomerOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer One [Member]</link:label>
    <link:label id="lab_trtn_CustomerOneMember_documentation_en-US" xlink:label="lab_trtn_CustomerOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CustomerOneMember" xlink:href="trtn-20241231.xsd#trtn_CustomerOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CustomerOneMember" xlink:to="lab_trtn_CustomerOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DesignatedCommonStockMember_303358f5-68a9-4037-bbe8-12de8176ac7b_terseLabel_en-US" xlink:label="lab_trtn_DesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Designated Common Stock</link:label>
    <link:label id="lab_trtn_DesignatedCommonStockMember_label_en-US" xlink:label="lab_trtn_DesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated Common Stock [Member]</link:label>
    <link:label id="lab_trtn_DesignatedCommonStockMember_documentation_en-US" xlink:label="lab_trtn_DesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Designated Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DesignatedCommonStockMember" xlink:href="trtn-20241231.xsd#trtn_DesignatedCommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DesignatedCommonStockMember" xlink:to="lab_trtn_DesignatedCommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_InvestmentTaxCreditPayment_e69be339-c2f3-4b27-b117-e0ca6da86b78_terseLabel_en-US" xlink:label="lab_trtn_InvestmentTaxCreditPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment tax credit, payment</link:label>
    <link:label id="lab_trtn_InvestmentTaxCreditPayment_label_en-US" xlink:label="lab_trtn_InvestmentTaxCreditPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Payment</link:label>
    <link:label id="lab_trtn_InvestmentTaxCreditPayment_documentation_en-US" xlink:label="lab_trtn_InvestmentTaxCreditPayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_InvestmentTaxCreditPayment" xlink:href="trtn-20241231.xsd#trtn_InvestmentTaxCreditPayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_InvestmentTaxCreditPayment" xlink:to="lab_trtn_InvestmentTaxCreditPayment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_98012650-5600-4a91-b543-40bf7427c206_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Add'l Paid in Capital (Deficit)</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock_036c5015-08b3-4433-937f-659fa5e6cc54_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of contractual maturities of the Company&#8217;s gross finance lease receivables</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_179f93f3-6683-46d2-bbae-2489f669ca28_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments_d9e84559-de18-4e59-b7da-e52211c6b950_terseLabel_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of permanent differences</link:label>
    <link:label id="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments_label_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Reconciliation, Permanent Differences and Other Adjustments</link:label>
    <link:label id="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments_documentation_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The portion of the difference, between total income tax expense or benefit as reported in the Income Statement for the year/accounting period and the expected income tax expense or benefit computed by applying the domestic federal statutory income tax rates to pretax income from continuing operations, that is attributable to permanent differences and all other items not otherwise listed in the existing taxonomy.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:href="trtn-20241231.xsd#trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:to="lab_trtn_IncomeTaxReconciliationPermanentDifferencesandOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_230d2258-53a3-4311-af2f-2cea88b81102_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Common stock dividends paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_71ae97a7-c1dc-4201-aef7-767a4a51a236_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Postemployment Benefits</link:label>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Benefits [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:to="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_658d99d1-0189-4c02-8e40-8065e453bd73_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityListingsExchangeAxis_7d2e83cd-1ecc-459f-8c40-2cba3034a2e2_terseLabel_en-US" xlink:label="lab_dei_EntityListingsExchangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Listings, Exchange [Axis]</link:label>
    <link:label id="lab_dei_EntityListingsExchangeAxis_label_en-US" xlink:label="lab_dei_EntityListingsExchangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Listings, Exchange [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityListingsExchangeAxis" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityListingsExchangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityListingsExchangeAxis" xlink:to="lab_dei_EntityListingsExchangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_7e06167f-3928-47ce-81d4-c78a226eb751_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Issued Accounting Standards Not Yet Adopted</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_5edb7641-50a4-4a36-ab44-64a5ba32dd61_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_0d5bfadd-293f-4968-81cb-e48d56d21cce_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.50% Series A Cumulative Redeemable Perpetual Preference Shares</link:label>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesAPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeriesAPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesAPreferredStockMember" xlink:to="lab_us-gaap_SeriesAPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_bd45519a-6d94-4fce-93bc-a9fe7cacd965_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_a67c65d8-b3c9-47af-a2e0-461c87d8ecd5_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_0c1b30bc-60fb-4409-a633-2696de70df80_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_PercentageOfOwnership_5d5c9e52-1116-4211-902a-147835d5bedc_terseLabel_en-US" xlink:label="lab_trtn_PercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of ownership</link:label>
    <link:label id="lab_trtn_PercentageOfOwnership_label_en-US" xlink:label="lab_trtn_PercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Ownership</link:label>
    <link:label id="lab_trtn_PercentageOfOwnership_documentation_en-US" xlink:label="lab_trtn_PercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage Of Ownership</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_PercentageOfOwnership" xlink:href="trtn-20241231.xsd#trtn_PercentageOfOwnership"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_PercentageOfOwnership" xlink:to="lab_trtn_PercentageOfOwnership" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_81a17baf-7385-4a41-a99c-d24b36e37f87_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EquipmentnetofsellingcostsMember_afe4b567-a615-4dae-a0b9-6a8fbf6afbbe_terseLabel_en-US" xlink:label="lab_trtn_EquipmentnetofsellingcostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment, net of selling costs</link:label>
    <link:label id="lab_trtn_EquipmentnetofsellingcostsMember_label_en-US" xlink:label="lab_trtn_EquipmentnetofsellingcostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment, net of selling costs [Member]</link:label>
    <link:label id="lab_trtn_EquipmentnetofsellingcostsMember_documentation_en-US" xlink:label="lab_trtn_EquipmentnetofsellingcostsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment, net of selling costs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EquipmentnetofsellingcostsMember" xlink:href="trtn-20241231.xsd#trtn_EquipmentnetofsellingcostsMember"/>
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    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_21b3cf90-2117-4d71-a416-4a7b4e51dd09_terseLabel_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax assets:</link:label>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ComponentsOfDeferredTaxAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:to="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MajorCustomersAxis_b979a538-6c9b-43ce-a826-44b6a34b57f2_terseLabel_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:label id="lab_srt_MajorCustomersAxis_label_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MajorCustomersAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MajorCustomersAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MajorCustomersAxis" xlink:to="lab_srt_MajorCustomersAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_77191d93-7bbd-46da-ac68-0cb5128aec54_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Three</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_498887a2-c956-4084-be97-dc34a58c9f2b_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CollectionAccountsAxis_a0c1214f-14fb-4cbb-816c-3ab66287c8af_terseLabel_en-US" xlink:label="lab_trtn_CollectionAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CollectionAccounts [Axis]</link:label>
    <link:label id="lab_trtn_CollectionAccountsAxis_label_en-US" xlink:label="lab_trtn_CollectionAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CollectionAccounts [Axis]</link:label>
    <link:label id="lab_trtn_CollectionAccountsAxis_documentation_en-US" xlink:label="lab_trtn_CollectionAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CollectionAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CollectionAccountsAxis" xlink:href="trtn-20241231.xsd#trtn_CollectionAccountsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CollectionAccountsAxis" xlink:to="lab_trtn_CollectionAccountsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareCashPaid_4820bdef-a753-44fd-b43f-45363441d69d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Per Share Payment (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_2f92ccf7-1a21-46c9-8a92-66d5eba61d28_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment arrangement, noncash expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTaxCredit_0ef7edb3-d71e-40fb-a17e-9225f5f0294b_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTaxCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment tax credit</link:label>
    <link:label id="lab_us-gaap_InvestmentTaxCredit_label_en-US" xlink:label="lab_us-gaap_InvestmentTaxCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Tax Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTaxCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentTaxCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTaxCredit" xlink:to="lab_us-gaap_InvestmentTaxCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_5a477f50-d1ba-4df4-9cdd-35129888b394_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_260cb71f-c539-4977-8153-9f395a784f6d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, equity instruments other than options, vested in period, fair value</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContingentConsiderationTypeDomain_afdc5e27-50d1-4e78-8d78-8e21ae50763c_terseLabel_en-US" xlink:label="lab_us-gaap_ContingentConsiderationTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Consideration Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ContingentConsiderationTypeDomain_label_en-US" xlink:label="lab_us-gaap_ContingentConsiderationTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingent Consideration Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContingentConsiderationTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ContingentConsiderationTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContingentConsiderationTypeDomain" xlink:to="lab_us-gaap_ContingentConsiderationTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_0230696c-3bf0-425c-b288-48ced0c7eb51_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_55fd339f-8adb-4a24-8efc-7c6d0a5fed27_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount_93050e48-f2b5-4c1d-a96e-c41d6c7dc661_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum contribution match</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Maximum Annual Contributions Per Employee, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeeAmount"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsNotDesignatedAsHedgingInstrumentsGainLossNet_81f3aae4-f033-4cc5-b70c-d40f553d6e27_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsNotDesignatedAsHedgingInstrumentsGainLossNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized loss on derivative instruments, net</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_cca19dc0-7634-4bb0-9758-f043e9e7851a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_5c3033f0-e220-424a-8e15-f9020fd8f34a_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireEquipmentOnLease_3b519cb3-d3ca-4b45-945b-db598427b301_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquipmentOnLease" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of leasing equipment and investments in finance leases</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquipmentOnLease_ead8f729-e3de-444f-95ba-22a5893f0885_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquipmentOnLease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of leasing equipment and investments in finance leases</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquipmentOnLease_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquipmentOnLease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equipment on Lease</link:label>
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    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_de3a1659-4e4b-498b-ba16-cd022dff863c_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other (income) expenses:</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_01230d1f-82f5-425f-a631-a63b3c1b712a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, interest rate, stated percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
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    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_cf89bf67-7b20-4282-b322-401693a733bd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of derivative instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_993fb56f-deda-4233-b2c9-3fa58f5f07c3_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
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    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_3a063522-6c2f-45df-9f60-7b2e9a31fca0_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">7.375% Series C Cumulative Redeemable Perpetual Preference Shares</link:label>
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    <link:label id="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_e61f08dc-9fb7-4e0b-bf04-9f796a32c01e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Compensation Costs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock"/>
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    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAfterYearFive_8ef67927-799b-45f6-8147-58348c518d74_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
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    <link:label id="lab_dei_AuditorFirmId_79c0d3e0-d973-4446-ac1e-617df59e9679_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_4ac832d4-78e6-48be-b515-c2312d4745ad_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in) investing activities</link:label>
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    <link:label id="lab_trtn_InterestRateSwapsAverageRemainingMaturity_label_en-US" xlink:label="lab_trtn_InterestRateSwapsAverageRemainingMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps Average Remaining Maturity</link:label>
    <link:label id="lab_trtn_InterestRateSwapsAverageRemainingMaturity_documentation_en-US" xlink:label="lab_trtn_InterestRateSwapsAverageRemainingMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted average remaining period until maturity of net outstanding interest rate swap agreements, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_InterestRateSwapsAverageRemainingMaturity" xlink:href="trtn-20241231.xsd#trtn_InterestRateSwapsAverageRemainingMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_InterestRateSwapsAverageRemainingMaturity" xlink:to="lab_trtn_InterestRateSwapsAverageRemainingMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_765e6fee-bf38-474b-8711-cc842b3b30df_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_8864262e-4d75-4555-83de-9a06117bb829_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets obtained in exchange for new operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_b1acf560-6923-4690-8919-b28b1fddab39_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_OperatingAndFinancingLeasesIncome_8d37212b-ae66-4a70-880d-88f92107d41b_totalLabel_en-US" xlink:label="lab_trtn_OperatingAndFinancingLeasesIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total leasing revenues</link:label>
    <link:label id="lab_trtn_OperatingAndFinancingLeasesIncome_0b7505bd-799f-49d1-ac6b-adbf221d85a5_terseLabel_en-US" xlink:label="lab_trtn_OperatingAndFinancingLeasesIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total leasing revenues:</link:label>
    <link:label id="lab_trtn_OperatingAndFinancingLeasesIncome_label_en-US" xlink:label="lab_trtn_OperatingAndFinancingLeasesIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating and Financing, Leases Income</link:label>
    <link:label id="lab_trtn_OperatingAndFinancingLeasesIncome_documentation_en-US" xlink:label="lab_trtn_OperatingAndFinancingLeasesIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of revenue recognized for the period from operating leases, including minimum lease revenue, contingent revenue, percentage revenue, sublease revenue and capital leases.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_OperatingAndFinancingLeasesIncome" xlink:href="trtn-20241231.xsd#trtn_OperatingAndFinancingLeasesIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_OperatingAndFinancingLeasesIncome" xlink:to="lab_trtn_OperatingAndFinancingLeasesIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_76fabbda-4cb3-428c-afc9-4fed2edb93d7_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_53d89668-f782-4664-84cc-3115e4c6385e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_d4de114b-a647-464e-8716-e4676dfdf88c_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_ca5b868d-9f58-4071-8e21-595121164ab4_totalLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_38653f92-a541-4389-8719-88aa744e82b5_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_dedef4a6-77a5-49c7-9ecb-73f2946d9a62_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LossgainAxisDomain_ffab64cc-f4ef-4df6-be38-8c01cdbb379e_terseLabel_en-US" xlink:label="lab_trtn_LossgainAxisDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Loss) gain [Axis] [Domain]</link:label>
    <link:label id="lab_trtn_LossgainAxisDomain_label_en-US" xlink:label="lab_trtn_LossgainAxisDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">(Loss) gain [Axis] [Domain]</link:label>
    <link:label id="lab_trtn_LossgainAxisDomain_documentation_en-US" xlink:label="lab_trtn_LossgainAxisDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for (Loss) gain [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LossgainAxisDomain" xlink:href="trtn-20241231.xsd#trtn_LossgainAxisDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LossgainAxisDomain" xlink:to="lab_trtn_LossgainAxisDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_5daf07f8-a82a-4107-8ee5-7fc1850330a2_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_49fee67e-fe62-4c78-b8c5-e756b3348c5e_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_b7d0fb0b-326b-4ab4-a24f-9f7a396a3c9d_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_3f07413f-4396-49c9-bc8f-c6c98e786947_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet_dcd7b69f-4ad5-4bce-aed9-6a181df285fc_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Realized (gains) losses</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) Reclassified from Accumulated OCI into Income, Effective Portion, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossReclassifiedFromAccumulatedOCIIntoIncomeEffectivePortionNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_622d789d-e44e-45fe-9fda-00bd35b44aa3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock_d1068507-5c12-4e54-bead-7b39c2808b7c_terseLabel_en-US" xlink:label="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of net book value of the Company's leasing equipment by equipment type</link:label>
    <link:label id="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock_label_en-US" xlink:label="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases, Finance Lease, Equipment Components [Table Text Block]</link:label>
    <link:label id="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock_documentation_en-US" xlink:label="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leases, Finance Lease, Equipment Components</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:href="trtn-20241231.xsd#trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:to="lab_trtn_LeasesFinanceLeaseEquipmentComponentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems_7cdfd55c-0d8e-4dc5-ba28-03960460e71c_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DefinedBenefitPlanDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:to="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForMergerRelatedCosts_709b85fe-51a2-4b69-9615-5ae3fda89afb_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments for merger related costs</link:label>
    <link:label id="lab_us-gaap_PaymentsForMergerRelatedCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsForMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Merger Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForMergerRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsForMergerRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForMergerRelatedCosts" xlink:to="lab_us-gaap_PaymentsForMergerRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_02195ef3-6aa6-4fdb-8143-22144ffb183d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND SHAREHOLDERS' EQUITY:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLocationAxis_6865812a-3031-4d70-91f3-78e8c47ec89e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Location [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLocationAxis_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLocationAxis" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_a3307280-b79e-4959-bd57-b1221c8d398c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_3aae2114-6be1-45df-9881-49c4c224e3f4_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.75% Series E Cumulative Redeemable Perpetual Preference Shares</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_95a032f8-f428-423a-9466-0afb3f6077b6_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LeasesRelatedAmortization_88e2f353-ba1c-459d-820c-1901a5c8ad5d_terseLabel_en-US" xlink:label="lab_trtn_LeasesRelatedAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease related amortization</link:label>
    <link:label id="lab_trtn_LeasesRelatedAmortization_label_en-US" xlink:label="lab_trtn_LeasesRelatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases Related Amortization</link:label>
    <link:label id="lab_trtn_LeasesRelatedAmortization_documentation_en-US" xlink:label="lab_trtn_LeasesRelatedAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leases Related Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LeasesRelatedAmortization" xlink:href="trtn-20241231.xsd#trtn_LeasesRelatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LeasesRelatedAmortization" xlink:to="lab_trtn_LeasesRelatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_43d9e8f7-4222-4596-a33e-267922eaf8e5_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_21bfe60b-27da-4a59-9eec-f1dd79e06fe1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_FinanceLeaseMember_324dfa78-9440-46b2-a451-3770fdaf747f_terseLabel_en-US" xlink:label="lab_trtn_FinanceLeaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease</link:label>
    <link:label id="lab_trtn_FinanceLeaseMember_label_en-US" xlink:label="lab_trtn_FinanceLeaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease [Member]</link:label>
    <link:label id="lab_trtn_FinanceLeaseMember_documentation_en-US" xlink:label="lab_trtn_FinanceLeaseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_FinanceLeaseMember" xlink:href="trtn-20241231.xsd#trtn_FinanceLeaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_FinanceLeaseMember" xlink:to="lab_trtn_FinanceLeaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_a875e74a-5db6-4f57-8d8d-74ad14031a84_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use asset - operating</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_47617ca8-8dfa-4e8b-900e-cb1a6e0ea85b_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EquipmentPurchasesPayable_c148ae33-9602-4546-b3b6-91ae461f7f85_terseLabel_en-US" xlink:label="lab_trtn_EquipmentPurchasesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment purchases payable</link:label>
    <link:label id="lab_trtn_EquipmentPurchasesPayable_1c374c7a-0e90-4206-8d05-a3e3de1984cb_verboseLabel_en-US" xlink:label="lab_trtn_EquipmentPurchasesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equipment purchases payable</link:label>
    <link:label id="lab_trtn_EquipmentPurchasesPayable_label_en-US" xlink:label="lab_trtn_EquipmentPurchasesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Purchases Payable</link:label>
    <link:label id="lab_trtn_EquipmentPurchasesPayable_documentation_en-US" xlink:label="lab_trtn_EquipmentPurchasesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The aggregate carrying value as of the balance sheet date of obligations attributable to purchases of leasing equipment for use as revenue earning assets, equipment purchased for resale activity or some combination thereof.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EquipmentPurchasesPayable" xlink:href="trtn-20241231.xsd#trtn_EquipmentPurchasesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_EquipmentPurchasesPayable" xlink:to="lab_trtn_EquipmentPurchasesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock_73a85622-ee94-4956-af2d-5fe88e04ceee_terseLabel_en-US" xlink:label="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Balance Sheet and Income Statement Effect</link:label>
    <link:label id="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock_label_en-US" xlink:label="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Balance Sheet and Income Statement Effect [Table Text Block]</link:label>
    <link:label id="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock_documentation_en-US" xlink:label="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Balance Sheet and Income Statement Effect [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:href="trtn-20241231.xsd#trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:to="lab_trtn_LesseeBalanceSheetandIncomeStatementEffectTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_e3431614-53d8-4393-b5a8-dff49aa357d7_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision (reversal) for doubtful accounts</link:label>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:to="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_e2a3f807-e9b1-4c1a-a8b5-5bb6c11860bd_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DividendDistributedToParent_06d884bb-2da9-424c-ada0-7f651ba8c6c5_terseLabel_en-US" xlink:label="lab_trtn_DividendDistributedToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend distributed to parent</link:label>
    <link:label id="lab_trtn_DividendDistributedToParent_label_en-US" xlink:label="lab_trtn_DividendDistributedToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Distributed to Parent</link:label>
    <link:label id="lab_trtn_DividendDistributedToParent_documentation_en-US" xlink:label="lab_trtn_DividendDistributedToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Distributed to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DividendDistributedToParent" xlink:href="trtn-20241231.xsd#trtn_DividendDistributedToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DividendDistributedToParent" xlink:to="lab_trtn_DividendDistributedToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_543f6141-5c71-4c4c-ab0f-17a67d838ce9_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award</link:label>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:to="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_0ad073d2-db2f-4dc5-b2de-9ef06f785d4e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument Risk [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_b7d7aef4-76d5-4cc7-985c-1d02c61eb5ea_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_e36109bd-c6c8-4105-b3d0-380e91f829eb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Outstanding (in thousands)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_ce3bb81b-cdae-45cd-b7ea-49b9345c5042_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_9e82d0e8-8c48-4973-a730-13d6f3a0d100_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_3223c752-c1e1-4c09-8b2b-a40ef9ce1de9_terseLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostsAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpensesAbstract" xlink:to="lab_us-gaap_CostsAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_IncomeTaxReconciliationDiscreteItems_fc6ff2c8-2739-45de-9c8c-a4a44822003a_terseLabel_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationDiscreteItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other discrete items</link:label>
    <link:label id="lab_trtn_IncomeTaxReconciliationDiscreteItems_label_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationDiscreteItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Reconciliation, Discrete Items</link:label>
    <link:label id="lab_trtn_IncomeTaxReconciliationDiscreteItems_documentation_en-US" xlink:label="lab_trtn_IncomeTaxReconciliationDiscreteItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Tax Reconciliation, Discrete Items</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_IncomeTaxReconciliationDiscreteItems" xlink:href="trtn-20241231.xsd#trtn_IncomeTaxReconciliationDiscreteItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_IncomeTaxReconciliationDiscreteItems" xlink:to="lab_trtn_IncomeTaxReconciliationDiscreteItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStock_244285ba-065f-45b2-9de6-6154bd2d3e04_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend on preferred shares</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStock_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStock" xlink:to="lab_us-gaap_DividendsPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_a8a00a8d-7cfd-4c46-8ae2-c7f0777f5966_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in derivative instruments designated as cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_9ba6afeb-fd1a-4957-809e-7bff5e847f7e_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock_6e50b04b-8002-42d0-841d-d00c763213d6_terseLabel_en-US" xlink:label="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Income Tax Interest and Penalties</link:label>
    <link:label id="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock_label_en-US" xlink:label="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Income Tax Interest and Penalties [Table Text Block]</link:label>
    <link:label id="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock_documentation_en-US" xlink:label="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summary of Income Tax Interest and Penalties [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:href="trtn-20241231.xsd#trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:to="lab_trtn_SummaryofIncomeTaxInterestandPenaltiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TreasuryStockPercentageAcquired_8a6486d5-e0c6-4ac1-8387-9c65faff1827_terseLabel_en-US" xlink:label="lab_trtn_TreasuryStockPercentageAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of treasury stock acquired</link:label>
    <link:label id="lab_trtn_TreasuryStockPercentageAcquired_label_en-US" xlink:label="lab_trtn_TreasuryStockPercentageAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Percentage Acquired</link:label>
    <link:label id="lab_trtn_TreasuryStockPercentageAcquired_documentation_en-US" xlink:label="lab_trtn_TreasuryStockPercentageAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Stock, Percentage Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TreasuryStockPercentageAcquired" xlink:href="trtn-20241231.xsd#trtn_TreasuryStockPercentageAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TreasuryStockPercentageAcquired" xlink:to="lab_trtn_TreasuryStockPercentageAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_68f3f17f-9869-46b9-8751-df69440c6d80_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_77a4d792-e6e7-4ead-b6a0-e386488ee90f_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAccountingStandard_e689244c-6208-405d-9dc4-3b35217c9391_terseLabel_en-US" xlink:label="lab_dei_DocumentAccountingStandard" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Accounting Standard</link:label>
    <link:label id="lab_dei_DocumentAccountingStandard_label_en-US" xlink:label="lab_dei_DocumentAccountingStandard" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Accounting Standard</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAccountingStandard" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentAccountingStandard"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAccountingStandard" xlink:to="lab_dei_DocumentAccountingStandard" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ImpairmentTable_b7f59992-3b2f-4887-b3da-674969916c4a_terseLabel_en-US" xlink:label="lab_trtn_ImpairmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment [Table]</link:label>
    <link:label id="lab_trtn_ImpairmentTable_label_en-US" xlink:label="lab_trtn_ImpairmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment [Table]</link:label>
    <link:label id="lab_trtn_ImpairmentTable_documentation_en-US" xlink:label="lab_trtn_ImpairmentTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ImpairmentTable" xlink:href="trtn-20241231.xsd#trtn_ImpairmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ImpairmentTable" xlink:to="lab_trtn_ImpairmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases_b36d31c0-0304-4146-9ef3-126dd6f5a6d7_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain (loss) on sale of leasing equipment</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Leased Assets, Net, Operating Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases" xlink:to="lab_us-gaap_GainLossOnSaleOfLeasedAssetsNetOperatingLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_c4c81702-f45a-43f8-b7eb-559b1938f42a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_SecruedDebtMember_2a59fd8b-de80-4661-9142-c7471b1aa805_terseLabel_en-US" xlink:label="lab_trtn_SecruedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total secured debt financings</link:label>
    <link:label id="lab_trtn_SecruedDebtMember_label_en-US" xlink:label="lab_trtn_SecruedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secrued Debt [Member]</link:label>
    <link:label id="lab_trtn_SecruedDebtMember_documentation_en-US" xlink:label="lab_trtn_SecruedDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secrued Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_SecruedDebtMember" xlink:href="trtn-20241231.xsd#trtn_SecruedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_SecruedDebtMember" xlink:to="lab_trtn_SecruedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_1096e44a-6d48-45fa-a479-7d41cc22a1fa_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_bd349319-f40d-43ac-b888-ea31f791817a_terseLabel_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:label id="lab_dei_EntitiesTable_label_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitiesTable" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitiesTable" xlink:to="lab_dei_EntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_28e126bb-68cb-4eda-84a6-46b060c63887_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other (income) expense, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour_9316c8a9-6e08-474d-958d-2d784d37732f_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Four</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_9d512a14-5567-43d3-8915-7289dcc6b62e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_dfed74fd-bdba-4346-a545-9ed1f9cd6ee7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_label_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:to="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears_c3d38213-6ee7-451e-a359-b1e2d87b6b13_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_353e2f1c-0911-4f3a-8881-31df91c7a204_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Preferred shares dividend declared</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_082161b0-f210-4c63-b5d3-f067d5882654_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RevenueEarningAssets_7116aab3-f52a-4152-97ac-1669e98719f1_totalLabel_en-US" xlink:label="lab_trtn_RevenueEarningAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Revenue earning assets</link:label>
    <link:label id="lab_trtn_RevenueEarningAssets_label_en-US" xlink:label="lab_trtn_RevenueEarningAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Earning Assets</link:label>
    <link:label id="lab_trtn_RevenueEarningAssets_documentation_en-US" xlink:label="lab_trtn_RevenueEarningAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets used to generate leasing revenue and gains on the sale of equipment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RevenueEarningAssets" xlink:href="trtn-20241231.xsd#trtn_RevenueEarningAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RevenueEarningAssets" xlink:to="lab_trtn_RevenueEarningAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock_526bb01d-0ffa-4e13-8f3b-be539ce7b3b8_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments Contingencies and Guarantees [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock" xlink:to="lab_us-gaap_CommitmentsContingenciesAndGuaranteesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AddressTypeDomain_b0449019-e93a-407e-b2fa-80d73e1ed668_terseLabel_en-US" xlink:label="lab_dei_AddressTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Address Type [Domain]</link:label>
    <link:label id="lab_dei_AddressTypeDomain_label_en-US" xlink:label="lab_dei_AddressTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Address Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AddressTypeDomain" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AddressTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AddressTypeDomain" xlink:to="lab_dei_AddressTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignEarningsRepatriated_fd90eb0b-47e3-43de-90db-20920de33b47_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignEarningsRepatriated" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unremitted earnings</link:label>
    <link:label id="lab_us-gaap_ForeignEarningsRepatriated_label_en-US" xlink:label="lab_us-gaap_ForeignEarningsRepatriated" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Earnings Repatriated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignEarningsRepatriated" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignEarningsRepatriated"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignEarningsRepatriated" xlink:to="lab_us-gaap_ForeignEarningsRepatriated" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CollectionAccountsDomain_5e46c7e7-94a9-4c8e-86dc-ca60f8dba4ae_terseLabel_en-US" xlink:label="lab_trtn_CollectionAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CollectionAccounts [Domain]</link:label>
    <link:label id="lab_trtn_CollectionAccountsDomain_label_en-US" xlink:label="lab_trtn_CollectionAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CollectionAccounts [Domain]</link:label>
    <link:label id="lab_trtn_CollectionAccountsDomain_documentation_en-US" xlink:label="lab_trtn_CollectionAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for CollectionAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CollectionAccountsDomain" xlink:href="trtn-20241231.xsd#trtn_CollectionAccountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CollectionAccountsDomain" xlink:to="lab_trtn_CollectionAccountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TaxCreditAgreementMember_013918e5-4004-425b-a758-61d6da82caea_terseLabel_en-US" xlink:label="lab_trtn_TaxCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Credit Agreement</link:label>
    <link:label id="lab_trtn_TaxCreditAgreementMember_label_en-US" xlink:label="lab_trtn_TaxCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Credit Agreement [Member]</link:label>
    <link:label id="lab_trtn_TaxCreditAgreementMember_documentation_en-US" xlink:label="lab_trtn_TaxCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Credit Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TaxCreditAgreementMember" xlink:href="trtn-20241231.xsd#trtn_TaxCreditAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TaxCreditAgreementMember" xlink:to="lab_trtn_TaxCreditAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_0c99ac08-92a3-4054-a550-1edd5ea05611_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_0ef55674-fb1f-4872-a42e-287a5f02d3ee_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesOutstanding_73832d77-faa6-493c-9fed-6ff4b6c380d9_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance, shares (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_04ba0f41-4a3b-47d3-94ab-bbdbb1fcd0b0_periodEndLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance, shares (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_label_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesOutstanding" xlink:to="lab_us-gaap_SharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TaxesWithhelldonUnremittedEarnings_96384f99-facf-4c01-86cb-5a69d42aa3e4_terseLabel_en-US" xlink:label="lab_trtn_TaxesWithhelldonUnremittedEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxes withhelld on unremitted earnings</link:label>
    <link:label id="lab_trtn_TaxesWithhelldonUnremittedEarnings_label_en-US" xlink:label="lab_trtn_TaxesWithhelldonUnremittedEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes Withhelld on Unremitted Earnings</link:label>
    <link:label id="lab_trtn_TaxesWithhelldonUnremittedEarnings_documentation_en-US" xlink:label="lab_trtn_TaxesWithhelldonUnremittedEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Taxes Withhelld on Unremitted Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TaxesWithhelldonUnremittedEarnings" xlink:href="trtn-20241231.xsd#trtn_TaxesWithhelldonUnremittedEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TaxesWithhelldonUnremittedEarnings" xlink:to="lab_trtn_TaxesWithhelldonUnremittedEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption_a0b6c90b-22d2-4f82-a9ca-15e2260fdc1e_totalLabel_en-US" xlink:label="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), net of tax</link:label>
    <link:label id="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption_label_en-US" xlink:label="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Loss, Net of Tax Including New Accounting Adoption</link:label>
    <link:label id="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption_documentation_en-US" xlink:label="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income Loss, Net of Tax Including New Accounting Adoption</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:href="trtn-20241231.xsd#trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:to="lab_trtn_OtherComprehensiveIncomeLossNetofTaxIncludingNewAccountingAdoption" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_c1d4637c-9dff-4c9e-9576-19775f948e87_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DeferredfinancecostPolicyTextBlock_173e352f-3208-4d9a-af17-16e9ce327e25_terseLabel_en-US" xlink:label="lab_trtn_DeferredfinancecostPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Costs</link:label>
    <link:label id="lab_trtn_DeferredfinancecostPolicyTextBlock_label_en-US" xlink:label="lab_trtn_DeferredfinancecostPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">deferred finance cost [Policy Text Block]</link:label>
    <link:label id="lab_trtn_DeferredfinancecostPolicyTextBlock_documentation_en-US" xlink:label="lab_trtn_DeferredfinancecostPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">deferred finance cost [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DeferredfinancecostPolicyTextBlock" xlink:href="trtn-20241231.xsd#trtn_DeferredfinancecostPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DeferredfinancecostPolicyTextBlock" xlink:to="lab_trtn_DeferredfinancecostPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_6c0e8a5e-c260-4ad5-ac44-9f0b35bc3d4b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net deferred income tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AmericasMember_a7685155-3509-440a-ab45-62de17b34027_terseLabel_en-US" xlink:label="lab_srt_AmericasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Americas</link:label>
    <link:label id="lab_srt_AmericasMember_label_en-US" xlink:label="lab_srt_AmericasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Americas [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AmericasMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_AmericasMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AmericasMember" xlink:to="lab_srt_AmericasMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_PreferredStockLiquidationPreferenceShare_049fdf1b-e2c5-4986-b88b-2580f4956968_terseLabel_en-US" xlink:label="lab_trtn_PreferredStockLiquidationPreferenceShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference Per Share</link:label>
    <link:label id="lab_trtn_PreferredStockLiquidationPreferenceShare_label_en-US" xlink:label="lab_trtn_PreferredStockLiquidationPreferenceShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Share</link:label>
    <link:label id="lab_trtn_PreferredStockLiquidationPreferenceShare_documentation_en-US" xlink:label="lab_trtn_PreferredStockLiquidationPreferenceShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_PreferredStockLiquidationPreferenceShare" xlink:href="trtn-20241231.xsd#trtn_PreferredStockLiquidationPreferenceShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_PreferredStockLiquidationPreferenceShare" xlink:to="lab_trtn_PreferredStockLiquidationPreferenceShare" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_BrookfieldInfrastructureMember_72f66e78-9ccd-49bb-ad4d-3681bcc2be71_terseLabel_en-US" xlink:label="lab_trtn_BrookfieldInfrastructureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Brookfield Infrastructure</link:label>
    <link:label id="lab_trtn_BrookfieldInfrastructureMember_label_en-US" xlink:label="lab_trtn_BrookfieldInfrastructureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Brookfield Infrastructure [Member]</link:label>
    <link:label id="lab_trtn_BrookfieldInfrastructureMember_documentation_en-US" xlink:label="lab_trtn_BrookfieldInfrastructureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Brookfield Infrastructure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_BrookfieldInfrastructureMember" xlink:href="trtn-20241231.xsd#trtn_BrookfieldInfrastructureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_BrookfieldInfrastructureMember" xlink:to="lab_trtn_BrookfieldInfrastructureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_63fa2e13-56bc-4c8f-8c40-bc8f996e1249_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Share repurchase to settle shareholder tax obligations (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_56186fea-59a1-4200-bbc8-3973223d641e_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_ae204b1f-52ef-4296-aa18-03e1b914118f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_2590acb2-c821-4f06-b23e-ad579de7c779_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TrustAccountsDomain_8b3fcfcb-3756-490b-8992-93238b92314a_terseLabel_en-US" xlink:label="lab_trtn_TrustAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TrustAccounts [Domain]</link:label>
    <link:label id="lab_trtn_TrustAccountsDomain_label_en-US" xlink:label="lab_trtn_TrustAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TrustAccounts [Domain]</link:label>
    <link:label id="lab_trtn_TrustAccountsDomain_documentation_en-US" xlink:label="lab_trtn_TrustAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for TrustAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TrustAccountsDomain" xlink:href="trtn-20241231.xsd#trtn_TrustAccountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TrustAccountsDomain" xlink:to="lab_trtn_TrustAccountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TriStarMember_e97aa577-6ceb-4d8d-b81a-6afe533bf291_terseLabel_en-US" xlink:label="lab_trtn_TriStarMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tristar</link:label>
    <link:label id="lab_trtn_TriStarMember_label_en-US" xlink:label="lab_trtn_TriStarMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TriStar [Member]</link:label>
    <link:label id="lab_trtn_TriStarMember_documentation_en-US" xlink:label="lab_trtn_TriStarMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">TriStar</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TriStarMember" xlink:href="trtn-20241231.xsd#trtn_TriStarMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TriStarMember" xlink:to="lab_trtn_TriStarMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_bfa518b0-38fe-463c-9f56-6e6584aafac1_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_be71aefb-34bd-4e0a-a261-686b62eb6396_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_ab0633c5-d1b2-44b2-83a2-a52104092f3d_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_OtherIncomeExpense_e0b4737b-2f2f-4bcb-bd72-7deeeb9b4b27_terseLabel_en-US" xlink:label="lab_trtn_OtherIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other (Income) Expense</link:label>
    <link:label id="lab_trtn_OtherIncomeExpense_label_en-US" xlink:label="lab_trtn_OtherIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other (Income) Expense</link:label>
    <link:label id="lab_trtn_OtherIncomeExpense_documentation_en-US" xlink:label="lab_trtn_OtherIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other (Income) Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_OtherIncomeExpense" xlink:href="trtn-20241231.xsd#trtn_OtherIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_OtherIncomeExpense" xlink:to="lab_trtn_OtherIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_622a4bf7-eda5-4829-9aaa-3591bff3855c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_0883733e-d3ba-41db-84d8-d2f414273aad_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Shares</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_TrustAccountsAxis_8ebf15d3-d0e7-47be-93ff-7634f951328c_terseLabel_en-US" xlink:label="lab_trtn_TrustAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TrustAccounts [Axis]</link:label>
    <link:label id="lab_trtn_TrustAccountsAxis_label_en-US" xlink:label="lab_trtn_TrustAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TrustAccounts [Axis]</link:label>
    <link:label id="lab_trtn_TrustAccountsAxis_documentation_en-US" xlink:label="lab_trtn_TrustAccountsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">TrustAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_TrustAccountsAxis" xlink:href="trtn-20241231.xsd#trtn_TrustAccountsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_TrustAccountsAxis" xlink:to="lab_trtn_TrustAccountsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_920b8c0c-344c-44a8-8e9a-db7697a38e05_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, equity instruments other than options, aggregate intrinsic value, outstanding</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_ad6e62d0-cafc-4e54-a81a-53f2abbc3925_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Common stock to Parent (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_e74dc127-b10c-4f98-a050-3b09748077ea_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving credit tranche</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_745121c8-2fff-475b-8944-6152dd307ab7_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_1538ea66-eee9-4f32-9162-b5ad3064dbff_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ImpairmentLineItems_e8110db3-47db-4d98-8c42-c6eba229412e_terseLabel_en-US" xlink:label="lab_trtn_ImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment [Line Items]</link:label>
    <link:label id="lab_trtn_ImpairmentLineItems_label_en-US" xlink:label="lab_trtn_ImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment [Line Items]</link:label>
    <link:label id="lab_trtn_ImpairmentLineItems_documentation_en-US" xlink:label="lab_trtn_ImpairmentLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Impairment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ImpairmentLineItems" xlink:href="trtn-20241231.xsd#trtn_ImpairmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ImpairmentLineItems" xlink:to="lab_trtn_ImpairmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_9d64a48a-9efe-4f78-8e1c-0e7ea6cb0c5f_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_74b67abc-1574-4be7-8e07-a3ed12a36c8b_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Intangible Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_8eb5e817-e6e4-4690-9bf5-9b66ce3651ed_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_BusinessContactMember_f022eaa6-1c7d-4795-84fe-659ef1f24f7f_terseLabel_en-US" xlink:label="lab_dei_BusinessContactMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Contact</link:label>
    <link:label id="lab_dei_BusinessContactMember_label_en-US" xlink:label="lab_dei_BusinessContactMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Contact [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_BusinessContactMember" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_BusinessContactMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_BusinessContactMember" xlink:to="lab_dei_BusinessContactMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_6b8799aa-4443-4178-943a-aa61683e7723_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_1ccf6de1-e65f-43eb-87a0-38bf5d4b9ea5_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_341b74d5-0a9c-440e-b565-3e1bcf8599ac_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_label_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:to="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_6d1a597c-a2ee-4065-a57d-7b67c565a793_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeneralAndAdministrativeExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_89161ec1-a369-48ef-bcd7-0724efd14281_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DerivativeImpactAxis_91f3f9f5-5c8d-4742-b034-4902a6902300_terseLabel_en-US" xlink:label="lab_trtn_DerivativeImpactAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Impact [Axis]</link:label>
    <link:label id="lab_trtn_DerivativeImpactAxis_label_en-US" xlink:label="lab_trtn_DerivativeImpactAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Impact [Axis]</link:label>
    <link:label id="lab_trtn_DerivativeImpactAxis_documentation_en-US" xlink:label="lab_trtn_DerivativeImpactAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Impact [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DerivativeImpactAxis" xlink:href="trtn-20241231.xsd#trtn_DerivativeImpactAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DerivativeImpactAxis" xlink:to="lab_trtn_DerivativeImpactAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CancellationOfCommonStockAmount_73d23035-2503-4a06-b3a3-02d42b4fe3a6_terseLabel_en-US" xlink:label="lab_trtn_CancellationOfCommonStockAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock</link:label>
    <link:label id="lab_trtn_CancellationOfCommonStockAmount_label_en-US" xlink:label="lab_trtn_CancellationOfCommonStockAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock, Amount</link:label>
    <link:label id="lab_trtn_CancellationOfCommonStockAmount_documentation_en-US" xlink:label="lab_trtn_CancellationOfCommonStockAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cancellation of Common Stock, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CancellationOfCommonStockAmount" xlink:href="trtn-20241231.xsd#trtn_CancellationOfCommonStockAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CancellationOfCommonStockAmount" xlink:to="lab_trtn_CancellationOfCommonStockAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems_4023991c-b192-4d91-9e56-5869e8aca2d7_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents Items [Line Items]</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents Items [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_2198c813-766a-4a8a-b2c0-a3a0b92c73d0_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing equipment, net of accumulated depreciation of $4,776,458 and $4,482,185</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_c68dce2d-a0fb-4f18-9e35-4688def71e3c_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Leasing equipment</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_f55ad857-49d8-4ee7-8721-f1d6a0739e78_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Equity Matters</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_f8dd0b8b-5563-4a9f-9932-34db506097f3_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and other accrued expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_78d11a7d-fb2e-49ae-998a-d08f2ef1c6f2_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_6f0a66ce-160e-40c7-a9db-0a54f4bc583e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree_eae0dfa8-c104-4c88-956d-f28e04ecce23_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Three</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RestrictedCashMinimumAmountRequirement_7a64f8bc-ca8a-444d-a0f5-71e6fed9e0fc_terseLabel_en-US" xlink:label="lab_trtn_RestrictedCashMinimumAmountRequirement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash, minimum amount requirement</link:label>
    <link:label id="lab_trtn_RestrictedCashMinimumAmountRequirement_label_en-US" xlink:label="lab_trtn_RestrictedCashMinimumAmountRequirement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Minimum Amount Requirement</link:label>
    <link:label id="lab_trtn_RestrictedCashMinimumAmountRequirement_documentation_en-US" xlink:label="lab_trtn_RestrictedCashMinimumAmountRequirement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash, Minimum Amount Requirement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RestrictedCashMinimumAmountRequirement" xlink:href="trtn-20241231.xsd#trtn_RestrictedCashMinimumAmountRequirement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RestrictedCashMinimumAmountRequirement" xlink:to="lab_trtn_RestrictedCashMinimumAmountRequirement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_6a506bc0-0298-45a4-92e4-a76892126b3d_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment and Geographic Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EquipmentTradingMember_9acb0242-001b-4f08-8b85-531b405c15e8_terseLabel_en-US" xlink:label="lab_trtn_EquipmentTradingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment Trading</link:label>
    <link:label id="lab_trtn_EquipmentTradingMember_label_en-US" xlink:label="lab_trtn_EquipmentTradingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Trading [Member]</link:label>
    <link:label id="lab_trtn_EquipmentTradingMember_documentation_en-US" xlink:label="lab_trtn_EquipmentTradingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the equipment trading segment of the entity which purchases containers from its shipping line customers and other sellers of containers and resells these containers to container retailers and users of containers for storage or one-way shipment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EquipmentTradingMember" xlink:href="trtn-20241231.xsd#trtn_EquipmentTradingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_EquipmentTradingMember" xlink:to="lab_trtn_EquipmentTradingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EquipmentHeldForSaleMember_fc02f1f4-2204-4701-bd74-f78378e63f8c_terseLabel_en-US" xlink:label="lab_trtn_EquipmentHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment Held For Sale</link:label>
    <link:label id="lab_trtn_EquipmentHeldForSaleMember_label_en-US" xlink:label="lab_trtn_EquipmentHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Held For Sale [Member]</link:label>
    <link:label id="lab_trtn_EquipmentHeldForSaleMember_documentation_en-US" xlink:label="lab_trtn_EquipmentHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment Held For Sale [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EquipmentHeldForSaleMember" xlink:href="trtn-20241231.xsd#trtn_EquipmentHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_EquipmentHeldForSaleMember" xlink:to="lab_trtn_EquipmentHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_32d14e70-f8d1-4725-9ad0-c69e62191d56_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_79de2012-ab14-4a9c-bda0-13197a76e185_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_531fe37e-1fbc-4656-a3e8-cbc21ee68e73_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_6cdf7a23-fb1b-494e-aae8-5fe6286e8972_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsDeclaredTableTextBlock_4f079931-99af-4f85-872e-7a7d2432552c_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends Declared</link:label>
    <link:label id="lab_us-gaap_DividendsDeclaredTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Declared [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsDeclaredTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsDeclaredTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsDeclaredTableTextBlock" xlink:to="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExaminationInterestExpense_4ffa2d58-1b43-4661-9cf9-f1f3700758cc_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExaminationInterestExpense_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Examination, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExaminationInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExaminationInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExaminationInterestExpense" xlink:to="lab_us-gaap_IncomeTaxExaminationInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemablePreferredStockDividends_9afd487f-a4dc-4443-a279-2ec06c004c8e_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemablePreferredStockDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: dividends on preferred shares</link:label>
    <link:label id="lab_us-gaap_RedeemablePreferredStockDividends_label_en-US" xlink:label="lab_us-gaap_RedeemablePreferredStockDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Preferred Stock Dividends</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities_8d5df34f-c190-4a15-b3ab-fffbe15d4b2d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities and other payables</link:label>
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    <link:label id="lab_us-gaap_InterestPaidNet_d1d4e422-43ca-4ff1-8a39-8ea10ff97f7b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
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    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_3cbbe665-2f06-4f35-8ae9-f3d67fc5b4b2_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and thereafter</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableTable_afc34dbf-f85f-4337-9aae-4f0af8b8e9f5_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends Payable [Table]</link:label>
    <link:label id="lab_us-gaap_DividendsPayableTable_label_en-US" xlink:label="lab_us-gaap_DividendsPayableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPayableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableTable" xlink:to="lab_us-gaap_DividendsPayableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_1977b9ab-7667-4bd9-8f0b-4d608f9ea1d4_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_fd277380-a5c4-474e-ab57-f61f6e43d70d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_b5118ec5-853f-4c03-bb95-3fb236953ba3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_f6885e09-9642-41c9-a621-6ef64db8ef98_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_83185bd9-9d5b-47a7-b1b8-9105a9ec3b11_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase commitment payable</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_00072c1d-c7b3-4bfe-9e21-2420a968399e_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_778ef466-a10c-4c8c-b9b4-ccd468daae07_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_93b66792-7c1a-443e-b282-eb56c4e30433_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_f9d7a814-c28e-4a36-80ca-f7663f509158_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_44dbb677-6cef-4ca2-8723-ffb5dcaef342_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_UndesignatedCommonStockMember_4895736b-f1ad-49fb-a72f-c4035a256bf2_terseLabel_en-US" xlink:label="lab_trtn_UndesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undesignated Common Stock</link:label>
    <link:label id="lab_trtn_UndesignatedCommonStockMember_label_en-US" xlink:label="lab_trtn_UndesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undesignated Common Stock [Member]</link:label>
    <link:label id="lab_trtn_UndesignatedCommonStockMember_documentation_en-US" xlink:label="lab_trtn_UndesignatedCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undesignated Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_UndesignatedCommonStockMember" xlink:href="trtn-20241231.xsd#trtn_UndesignatedCommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_UndesignatedCommonStockMember" xlink:to="lab_trtn_UndesignatedCommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_026c6b73-afb6-46e1-964f-eeca3a94e86c_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI_a6d02709-60b0-4e6b-8438-ba60bacdb098_terseLabel_en-US" xlink:label="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred partnership income (loss)</link:label>
    <link:label id="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI_label_en-US" xlink:label="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Investment in TCI</link:label>
    <link:label id="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI_documentation_en-US" xlink:label="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Investment in TCI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:href="trtn-20241231.xsd#trtn_DeferredTaxLiabilitiesInvestmentinTCI"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:to="lab_trtn_DeferredTaxLiabilitiesInvestmentinTCI" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_a5397c50-05a2-4766-9f13-e76a57944114_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths_c4d67ba2-0efb-4ef5-a894-ea3850fe2d1c_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flow hedge gain (loss) to be reclassified within 12 months</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedge Gain (Loss) to be Reclassified within 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_1f0396aa-eb6a-4fb3-881b-72a5c33e5f12_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesRetired_ba5af1c1-a3b1-4b0d-9590-817a533199a1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesRetired" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cancellation of Treasury Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesRetired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesRetired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Retired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesRetired" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockSharesRetired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesRetired" xlink:to="lab_us-gaap_TreasuryStockSharesRetired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_b692618e-9352-442e-88c1-932bac135aea_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of debt instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_738f4e7d-b8de-4fc2-aef6-e0b8e1a86b4c_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_d3993ada-67a3-4e11-a5c0-851c57f72b2c_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_655c927e-0de9-4b89-901e-4021eee8fbe4_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_15578fed-c709-4712-adfd-411807d22314_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liability - operating</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_606e2fbb-f299-4733-8611-8e9ac3b0dfd9_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total present value of lease liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_AssetBackedWarehouseFacilityMember_2ab3429f-0286-42a7-a043-a7a770fa03ea_terseLabel_en-US" xlink:label="lab_trtn_AssetBackedWarehouseFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed securitization warehouse</link:label>
    <link:label id="lab_trtn_AssetBackedWarehouseFacilityMember_label_en-US" xlink:label="lab_trtn_AssetBackedWarehouseFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Backed Warehouse Facility [Member]</link:label>
    <link:label id="lab_trtn_AssetBackedWarehouseFacilityMember_documentation_en-US" xlink:label="lab_trtn_AssetBackedWarehouseFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents warehouse credit facility which is collateralized by a specific group of underlying assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_AssetBackedWarehouseFacilityMember" xlink:href="trtn-20241231.xsd#trtn_AssetBackedWarehouseFacilityMember"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_7553a99c-31d5-43ba-ba17-ca87455259ad_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod_8078b0a5-1528-4cf9-bbfb-fee804b8122e_terseLabel_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Fixed Leg (Pay) Interest Rate</link:label>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod_label_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Notional Amount of Interest Rate During Period</link:label>
    <link:label id="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod_documentation_en-US" xlink:label="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Notional Amount of Interest Rate During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:href="trtn-20241231.xsd#trtn_NetNotionalAmountofInterestRateDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:to="lab_trtn_NetNotionalAmountofInterestRateDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_RestrictedCashAccountsDomain_88e1ac9a-9994-4969-96d1-57b94217be41_terseLabel_en-US" xlink:label="lab_trtn_RestrictedCashAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RestrictedCashAccounts [Domain]</link:label>
    <link:label id="lab_trtn_RestrictedCashAccountsDomain_label_en-US" xlink:label="lab_trtn_RestrictedCashAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">RestrictedCashAccounts [Domain]</link:label>
    <link:label id="lab_trtn_RestrictedCashAccountsDomain_documentation_en-US" xlink:label="lab_trtn_RestrictedCashAccountsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for RestrictedCashAccounts [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_RestrictedCashAccountsDomain" xlink:href="trtn-20241231.xsd#trtn_RestrictedCashAccountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_RestrictedCashAccountsDomain" xlink:to="lab_trtn_RestrictedCashAccountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_11a70286-e8e3-4817-b0f9-694fff839124_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectOperatingCosts_e3ab7522-baac-4cc9-b5a9-1c517628be81_terseLabel_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct operating expenses</link:label>
    <link:label id="lab_us-gaap_DirectOperatingCosts_label_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Operating Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectOperatingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DirectOperatingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectOperatingCosts" xlink:to="lab_us-gaap_DirectOperatingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_d12e406d-e8f9-48d8-bc14-b3e9c5612c6f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common shares dividend declared</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_5be3e9fc-54a3-4a8b-bed8-6608c9b49ae6_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash dividend</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_20631e2f-fe3e-4d2d-b102-3d4431769987_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_202eeefb-b0ba-4a4f-9fa4-0d135b004497_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract_3549d29a-73e2-4a8e-880e-c4e8671da326_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_7727c787-d03a-4242-9ef9-6e1853150048_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_3d7d2ad2-533c-45f3-be10-5765acd65f31_verboseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_787d34ba-6bea-4ed3-92cd-00206316e066_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Trading margin</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_aea5cce6-ae1d-462b-8bee-659403ed81af_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_72cfddca-dbad-4470-a3de-919c266d1bac_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_00bdeebb-d364-4963-a5ab-cf7f6c08170c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_09fe1695-d060-4aa6-98cc-3ffecba37309_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_bdedf6b1-164a-4509-aad8-29b7cfdebff1_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_d1b851db-ff77-4fa3-adde-562f04a31fa8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_af534462-dee8-4861-9059-cdb33592aeb1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_5c6e26d8-a9c3-4747-a6b8-dff0423de99c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, Unamortized Deferred Financing Costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_cdc8205e-1a38-44e3-9ca4-48f44121230a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized debt costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_c71f2ad2-7cad-4861-a0d6-43e0e47761e6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_27994b6a-ce55-4fc7-89ad-e99509b3e2be_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment, Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_c01fdce5-39cc-4ecf-b40f-407a91b11a1f_verboseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit_0e5d5161-39bd-4626-88e3-76f45f98dbb6_terseLabel_en-US" xlink:label="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, accordion feature, increase limit</link:label>
    <link:label id="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit_label_en-US" xlink:label="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:label id="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit_documentation_en-US" xlink:label="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of credit facility, accordion feature, increase limit, subject to certain conditions by obtaining additional commitments from existing and/or new lenders.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:href="trtn-20241231.xsd#trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:to="lab_trtn_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_556b9299-0140-4bc4-9396-63d1d1e6dfad_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy_053c8302-322d-4483-be94-55aa73a2b0fc_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Investment in Finance Leases</link:label>
    <link:label id="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLoansAndLeasesReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:to="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_0a5eaa60-a67c-4641-974b-fa3b106f4b3f_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Common stock to Parent</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_26f0d39c-952a-4ab4-863a-a059eb769c01_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_e6538141-2099-428f-9b69-70beb8f15f30_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_FixedandHedgedDebtMember_680a2a9f-5d32-47df-8ef5-1c847a70127d_terseLabel_en-US" xlink:label="lab_trtn_FixedandHedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed and Hedged Debt</link:label>
    <link:label id="lab_trtn_FixedandHedgedDebtMember_label_en-US" xlink:label="lab_trtn_FixedandHedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed and Hedged Debt [Member]</link:label>
    <link:label id="lab_trtn_FixedandHedgedDebtMember_documentation_en-US" xlink:label="lab_trtn_FixedandHedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed and Hedged Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_FixedandHedgedDebtMember" xlink:href="trtn-20241231.xsd#trtn_FixedandHedgedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_FixedandHedgedDebtMember" xlink:to="lab_trtn_FixedandHedgedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_4d4804a0-254c-4a32-bf15-243616d7943e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_79f7df91-fdf0-4e2e-b80f-e6150d33a0e1_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_260d3e66-7595-410a-898e-64ed64132871_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_d2163e3c-ba47-462f-876a-661c9b1348f1_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common shares, $0.01 par value, 250,000,000 and 270,000,000 shares authorized, 101,158,891 shares issued and outstanding</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_0bab2eb9-2e0e-43a0-8b90-7bb608da980e_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_label_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFinStmtErrorCorrectionFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:to="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDerivatives_a1f77256-acbe-4f63-a335-fbaf6d398895_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDerivatives_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxLiabilitiesDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts_f00e2b7a-9c0b-4fb0-9607-ecde1d31a7a3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, integration related costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Integration Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationIntegrationRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationIntegrationRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_PropertyAvailableForOperatingLeaseNet_ada92f6a-211b-40ae-8f90-044d3b04f1b9_terseLabel_en-US" xlink:label="lab_trtn_PropertyAvailableForOperatingLeaseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property available for operating lease, net</link:label>
    <link:label id="lab_trtn_PropertyAvailableForOperatingLeaseNet_label_en-US" xlink:label="lab_trtn_PropertyAvailableForOperatingLeaseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Available for Operating Lease, Net</link:label>
    <link:label id="lab_trtn_PropertyAvailableForOperatingLeaseNet_documentation_en-US" xlink:label="lab_trtn_PropertyAvailableForOperatingLeaseNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of property available for lease, net of accumulated depreciation, as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_PropertyAvailableForOperatingLeaseNet" xlink:href="trtn-20241231.xsd#trtn_PropertyAvailableForOperatingLeaseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_PropertyAvailableForOperatingLeaseNet" xlink:to="lab_trtn_PropertyAvailableForOperatingLeaseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DryContainerUnitsMember_3b4ac944-9307-4719-8e50-d92bc04e2925_terseLabel_en-US" xlink:label="lab_trtn_DryContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dry container</link:label>
    <link:label id="lab_trtn_DryContainerUnitsMember_label_en-US" xlink:label="lab_trtn_DryContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dry Container Units [Member]</link:label>
    <link:label id="lab_trtn_DryContainerUnitsMember_documentation_en-US" xlink:label="lab_trtn_DryContainerUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents dry containers, which are depreciable revenue earnings assets used to carry general cargo such as manufactured component parts, consumer staples, electronics and apparel.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DryContainerUnitsMember" xlink:href="trtn-20241231.xsd#trtn_DryContainerUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DryContainerUnitsMember" xlink:to="lab_trtn_DryContainerUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_012ecc70-8f29-4a2e-9978-4ea786aa607b_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MajorPropertyClassAxis_7ebbff4f-1b8f-4efd-9c93-b8e12690ad77_terseLabel_en-US" xlink:label="lab_us-gaap_MajorPropertyClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Major Property Class [Axis]</link:label>
    <link:label id="lab_us-gaap_MajorPropertyClassAxis_label_en-US" xlink:label="lab_us-gaap_MajorPropertyClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Major Property Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MajorPropertyClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MajorPropertyClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MajorPropertyClassAxis" xlink:to="lab_us-gaap_MajorPropertyClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock_1b6e7e86-2689-4f93-92e0-7f562b861b8c_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeasesOfLessorDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:to="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_NetTradingMargin_0045041a-9cb1-4955-ae35-022b42549183_terseLabel_en-US" xlink:label="lab_trtn_NetTradingMargin" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net trading margin</link:label>
    <link:label id="lab_trtn_NetTradingMargin_label_en-US" xlink:label="lab_trtn_NetTradingMargin" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Trading Margin</link:label>
    <link:label id="lab_trtn_NetTradingMargin_documentation_en-US" xlink:label="lab_trtn_NetTradingMargin" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Trading Margin</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_NetTradingMargin" xlink:href="trtn-20241231.xsd#trtn_NetTradingMargin"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_NetTradingMargin" xlink:to="lab_trtn_NetTradingMargin" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent_f66ea0fe-f68b-4204-9fb0-344d6a619f1d_terseLabel_en-US" xlink:label="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of uncertain tax positions</link:label>
    <link:label id="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent_label_en-US" xlink:label="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Uncertain Tax Positions, Percent</link:label>
    <link:label id="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent_documentation_en-US" xlink:label="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Uncertain Tax Positions, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:href="trtn-20241231.xsd#trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:to="lab_trtn_EffectiveIncomeTaxRateReconciliationUncertainTaxPositionsPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_044c9752-1579-494b-b9e5-eb83e2438aef_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_PaymentsReceiptstoTerminateDerivatives_62167214-76f0-4b4d-90be-1b8aa19a314e_terseLabel_en-US" xlink:label="lab_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash received (paid) for settlement of interest rate swaps</link:label>
    <link:label id="lab_trtn_PaymentsReceiptstoTerminateDerivatives_label_en-US" xlink:label="lab_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">(Payments) Receipts to Terminate Derivatives</link:label>
    <link:label id="lab_trtn_PaymentsReceiptstoTerminateDerivatives_documentation_en-US" xlink:label="lab_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The settlement price or receivable on the termination of designated (whose change in fair value was not included in earnings) and non-designated (whose change in fair value was included in earnings) interest rate swap agreements.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:href="trtn-20241231.xsd#trtn_PaymentsReceiptstoTerminateDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:to="lab_trtn_PaymentsReceiptstoTerminateDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExaminationPenaltiesExpense_307b3f4c-1d3e-4a03-a30b-fdf0efdec8b0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationPenaltiesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Penalty expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExaminationPenaltiesExpense_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationPenaltiesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Examination, Penalties Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExaminationPenaltiesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExaminationPenaltiesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExaminationPenaltiesExpense" xlink:to="lab_us-gaap_IncomeTaxExaminationPenaltiesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_ReclassificationOfShareBasedAwardsToALiability_1e995ed8-4f99-45d8-9012-b377d4f3bfc1_terseLabel_en-US" xlink:label="lab_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of share-based awards to a liability</link:label>
    <link:label id="lab_trtn_ReclassificationOfShareBasedAwardsToALiability_label_en-US" xlink:label="lab_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification of Share-Based Awards to a Liability</link:label>
    <link:label id="lab_trtn_ReclassificationOfShareBasedAwardsToALiability_documentation_en-US" xlink:label="lab_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reclassification of Share-Based Awards to a Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:href="trtn-20241231.xsd#trtn_ReclassificationOfShareBasedAwardsToALiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:to="lab_trtn_ReclassificationOfShareBasedAwardsToALiability" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_1d407acd-be17-480a-bc0e-1d0135877848_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_UnhedgedDebtMember_84db4786-5a7f-4b63-9bcb-0c97134fee12_terseLabel_en-US" xlink:label="lab_trtn_UnhedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unhedged Debt</link:label>
    <link:label id="lab_trtn_UnhedgedDebtMember_label_en-US" xlink:label="lab_trtn_UnhedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unhedged Debt [Member]</link:label>
    <link:label id="lab_trtn_UnhedgedDebtMember_documentation_en-US" xlink:label="lab_trtn_UnhedgedDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unhedged Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_UnhedgedDebtMember" xlink:href="trtn-20241231.xsd#trtn_UnhedgedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_UnhedgedDebtMember" xlink:to="lab_trtn_UnhedgedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_1e643c87-19de-481a-9680-7d123ea3da76_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_4dec349a-30ac-404b-be69-19a0b8fc6688_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred shares, $0.01 par value, at liquidation preference</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_HedgedVariableRateDebtMember_1bbe9ebb-152e-4242-86bd-fac0b6455050_terseLabel_en-US" xlink:label="lab_trtn_HedgedVariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedged Variable Rate Debt</link:label>
    <link:label id="lab_trtn_HedgedVariableRateDebtMember_label_en-US" xlink:label="lab_trtn_HedgedVariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Variable Rate Debt [Member]</link:label>
    <link:label id="lab_trtn_HedgedVariableRateDebtMember_documentation_en-US" xlink:label="lab_trtn_HedgedVariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Variable Rate Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_HedgedVariableRateDebtMember" xlink:href="trtn-20241231.xsd#trtn_HedgedVariableRateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_HedgedVariableRateDebtMember" xlink:to="lab_trtn_HedgedVariableRateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_SavingsPlanAbstract_092a50c9-70b7-46cd-8dc3-1f1b21dde339_terseLabel_en-US" xlink:label="lab_trtn_SavingsPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings Plan [Abstract]</link:label>
    <link:label id="lab_trtn_SavingsPlanAbstract_label_en-US" xlink:label="lab_trtn_SavingsPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Savings Plan [Abstract]</link:label>
    <link:label id="lab_trtn_SavingsPlanAbstract_documentation_en-US" xlink:label="lab_trtn_SavingsPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Savings Plan [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_SavingsPlanAbstract" xlink:href="trtn-20241231.xsd#trtn_SavingsPlanAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_SavingsPlanAbstract" xlink:to="lab_trtn_SavingsPlanAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_a32826ad-d745-4307-a9be-79b298f04a2f_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, useful life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_00df20f4-5ed6-491e-a9db-afd5ff50cff6_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_8da6d712-33d1-4cd9-b17c-cd252f66f423_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, payments</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_VariableRateDebtMember_81ea99ae-3bd9-4733-aa39-dcc34076062a_terseLabel_en-US" xlink:label="lab_trtn_VariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate Debt</link:label>
    <link:label id="lab_trtn_VariableRateDebtMember_label_en-US" xlink:label="lab_trtn_VariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate Debt [Member]</link:label>
    <link:label id="lab_trtn_VariableRateDebtMember_documentation_en-US" xlink:label="lab_trtn_VariableRateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Rate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_VariableRateDebtMember" xlink:href="trtn-20241231.xsd#trtn_VariableRateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_VariableRateDebtMember" xlink:to="lab_trtn_VariableRateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsDeferredIncome_b559ff27-5721-4f43-a100-c63be2508a3c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsDeferredIncome_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Deferred Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsDeferredIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:to="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_6169d1e4-50db-4d55-b3a1-d9a41bcd6400_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets, operating loss carryforwards, domestic</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Domestic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableLineItems_02e9cc71-81ff-403c-ae47-7846ab072cd9_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends Payable [Line Items]</link:label>
    <link:label id="lab_us-gaap_DividendsPayableLineItems_label_en-US" xlink:label="lab_us-gaap_DividendsPayableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendsPayableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableLineItems" xlink:to="lab_us-gaap_DividendsPayableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_542484c3-2fac-4547-a0be-2ee4eef522f9_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_1c7048ab-b496-4ed0-87f5-4be37b3a8788_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_b8c8b84e-3fa6-4685-9488-ae018bff40cb_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Furniture and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_73144c45-9203-4e18-89af-92c78b9db0a6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_b0343d9f-4f3f-4828-9b27-bba5d70c8717_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_18d8a918-b172-47a1-9330-f036aabcccb4_verboseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_b7197367-c41a-4f46-8643-b8c317a1bf0c_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_f1477661-9d21-4210-86c0-cf5259de1fc9_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Volatility</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Weighted Average Volatility Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_249a6b99-a866-4a8d-bac0-57c61475b87a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equipment trading expenses</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_757e80d3-1d3d-482d-9b20-4285d539d59a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DirectFinancingLeaseReceivableMember_82c3bf60-13f8-420d-b464-81e407bd6a55_terseLabel_en-US" xlink:label="lab_trtn_DirectFinancingLeaseReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct Financing Lease Receivable</link:label>
    <link:label id="lab_trtn_DirectFinancingLeaseReceivableMember_label_en-US" xlink:label="lab_trtn_DirectFinancingLeaseReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Financing Lease Receivable [Member]</link:label>
    <link:label id="lab_trtn_DirectFinancingLeaseReceivableMember_documentation_en-US" xlink:label="lab_trtn_DirectFinancingLeaseReceivableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Direct Financing Lease Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DirectFinancingLeaseReceivableMember" xlink:href="trtn-20241231.xsd#trtn_DirectFinancingLeaseReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DirectFinancingLeaseReceivableMember" xlink:to="lab_trtn_DirectFinancingLeaseReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_de908eae-a97c-43b4-acf4-6f841498ea48_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_c17d677a-6e19-4eab-8b69-b30bceb4788e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDividendsPayableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_602bbd1c-e3f0-4f38-b079-0f21886b75f4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Description of the Business and Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Description and Basis of Presentation [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:to="lab_us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_8ea2e363-d8fa-4731-8d86-2b888a772523_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_b0e515fe-b957-4dd5-a3ed-a9e672fa2644_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
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    <link:label id="lab_us-gaap_Revenues_8a699809-e47f-402c-ae2d-da6b07ec31f6_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment trading revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_94cb1703-3b48-43a4-a01b-15e93234eed0_verboseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total equipment trading revenues:</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_0eeb9631-711d-446d-a416-6dde898ef58b_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_6f453de8-c820-41d2-803d-8e644e2cbf86_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_299ded91-354b-45d7-9775-ac1f5fac69ff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on preferred shares</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock"/>
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    <link:label id="lab_us-gaap_NondesignatedMember_e2bbb09c-9e29-42a5-a456-1bba42397f7a_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_237281dd-8d97-4ac3-899a-24ba44a23b3a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_884edb7c-4809-464d-8956-600336772084_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CumulativeDividends_a3e41104-a283-4b7a-ba49-37e49ae07d6c_terseLabel_en-US" xlink:label="lab_us-gaap_CumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative dividends</link:label>
    <link:label id="lab_us-gaap_CumulativeDividends_label_en-US" xlink:label="lab_us-gaap_CumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cumulative Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CumulativeDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CumulativeDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CumulativeDividends" xlink:to="lab_us-gaap_CumulativeDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths_90ebfcbb-6d97-4b89-b67a-2f411331999b_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_269fc637-903c-4f9c-915e-c59e5f6ff157_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_50de1eb3-0021-47d9-a04a-56dabff8ea27_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment Held for Sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_332825c2-a4e1-4fa4-b1c6-8d895fdc938a_verboseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other non-cash compensation costs</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_5de9487d-c225-40be-847a-62f7c8b4a319_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease related deferrals</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
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    <link:label id="lab_us-gaap_NetIncomeLoss_33c5d610-b593-4e7b-b8cb-deb3f423147f_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_UndesignatedSharesValueIssued_d5a80b72-a2b8-4a2c-83c7-3229f81ed646_terseLabel_en-US" xlink:label="lab_trtn_UndesignatedSharesValueIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undesignated shares, $0.01 par value, 20,800,000 and 800,000 shares authorized, no shares issued and outstanding</link:label>
    <link:label id="lab_trtn_UndesignatedSharesValueIssued_label_en-US" xlink:label="lab_trtn_UndesignatedSharesValueIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undesignated Shares, Value, Issued</link:label>
    <link:label id="lab_trtn_UndesignatedSharesValueIssued_documentation_en-US" xlink:label="lab_trtn_UndesignatedSharesValueIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undesignated Shares, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_UndesignatedSharesValueIssued" xlink:href="trtn-20241231.xsd#trtn_UndesignatedSharesValueIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_UndesignatedSharesValueIssued" xlink:to="lab_trtn_UndesignatedSharesValueIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_30737d55-edc6-43d4-be65-929fb0afa6df_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCountryMember_c6fdd051-38ab-42db-8584-623aa59daee9_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_ForeignCountryMember_label_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCountryMember" xlink:to="lab_us-gaap_ForeignCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock_b9071a0f-84be-4246-a8e7-8f6e16735e0a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of components of the net investment in finance leases</link:label>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Components of Leveraged Lease Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfComponentsOfLeveragedLeaseInvestmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_778d0a45-feec-490e-af6f-6554655c115c_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_AssetsHeldForSalePolicyTextBlock_3c18009a-a3ff-4b3d-855b-103fda08a3da_terseLabel_en-US" xlink:label="lab_trtn_AssetsHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment Held for Sale</link:label>
    <link:label id="lab_trtn_AssetsHeldForSalePolicyTextBlock_label_en-US" xlink:label="lab_trtn_AssetsHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Held for Sale [Policy Text Block]</link:label>
    <link:label id="lab_trtn_AssetsHeldForSalePolicyTextBlock_documentation_en-US" xlink:label="lab_trtn_AssetsHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of the accounting policy for equipment returned off lease and reclassified to equipment held for sale, which is expected to be sold in less than one year.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_AssetsHeldForSalePolicyTextBlock" xlink:href="trtn-20241231.xsd#trtn_AssetsHeldForSalePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_AssetsHeldForSalePolicyTextBlock" xlink:to="lab_trtn_AssetsHeldForSalePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesBPreferredStockMember_5961f1a1-07f2-4277-a0f6-3beef36bbe71_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesBPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.00% Series B Cumulative Redeemable Perpetual Preference Shares</link:label>
    <link:label id="lab_us-gaap_SeriesBPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesBPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesBPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeriesBPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesBPreferredStockMember" xlink:to="lab_us-gaap_SeriesBPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_855a4749-a093-4171-9d09-5c8dc22c4032_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_2b4c3d86-3710-4862-b9cf-e79ea73d61da_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_b1d354cc-370f-4132-930e-368c57736bc9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_b901a1b1-dbe5-43e0-a752-66fe8b76aaf8_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Treasury shares acquired</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockValueAcquiredCostMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:to="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine3_157d814b-4615-4083-a367-5d81c8b4c622_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Three</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine3_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine3" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine3" xlink:to="lab_dei_EntityAddressAddressLine3" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_6c11e869-e903-4511-b62a-5ea575fdbbde_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_becf2696-6afa-43f3-8927-985b30ddd6e4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_22f52e94-a345-4425-a4e3-54b68e8417f3_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Remaining Lease Term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_16430570-e218-454f-b38d-71a43b966daa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized debt premium &amp; discounts</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_a83afe57-82e5-4b68-a4f0-ce47fd3409f4_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_d4846b72-7d13-44d0-b9b5-a43784cdccdc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of interest rate swap contracts</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Derivatives [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContingentConsiderationByTypeAxis_5d8428aa-5ee9-4f27-be5e-70576bf1f531_terseLabel_en-US" xlink:label="lab_us-gaap_ContingentConsiderationByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Consideration by Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ContingentConsiderationByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ContingentConsiderationByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingent Consideration by Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContingentConsiderationByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ContingentConsiderationByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContingentConsiderationByTypeAxis" xlink:to="lab_us-gaap_ContingentConsiderationByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_9aa0c335-986b-4bcc-a1f3-a217402a2711_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total undiscounted future cash flows related to lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract_9d8f663e-7d03-4f2c-88ae-a31374c9c972_terseLabel_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax liabilities:</link:label>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:to="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_CustomerThreeMember_37a4da44-68e0-4d80-9528-66b7c6dd75fa_terseLabel_en-US" xlink:label="lab_trtn_CustomerThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Three</link:label>
    <link:label id="lab_trtn_CustomerThreeMember_label_en-US" xlink:label="lab_trtn_CustomerThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Three [Member]</link:label>
    <link:label id="lab_trtn_CustomerThreeMember_documentation_en-US" xlink:label="lab_trtn_CustomerThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_CustomerThreeMember" xlink:href="trtn-20241231.xsd#trtn_CustomerThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_CustomerThreeMember" xlink:to="lab_trtn_CustomerThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredRevenue_d405c47b-ef55-4bd1-9409-0e7fc4e5860c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredRevenue_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Deferred Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDeferredRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInDeferredRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDeferredRevenue" xlink:to="lab_us-gaap_IncreaseDecreaseInDeferredRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_DebtPercentageInterestRateRemainingTerm_16930c4e-2f1f-4652-b57f-c675f4412705_terseLabel_en-US" xlink:label="lab_trtn_DebtPercentageInterestRateRemainingTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Avg Remaining Term</link:label>
    <link:label id="lab_trtn_DebtPercentageInterestRateRemainingTerm_label_en-US" xlink:label="lab_trtn_DebtPercentageInterestRateRemainingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Percentage Interest Rate Remaining Term</link:label>
    <link:label id="lab_trtn_DebtPercentageInterestRateRemainingTerm_documentation_en-US" xlink:label="lab_trtn_DebtPercentageInterestRateRemainingTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Percentage Interest Rate Remaining Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_DebtPercentageInterestRateRemainingTerm" xlink:href="trtn-20241231.xsd#trtn_DebtPercentageInterestRateRemainingTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_DebtPercentageInterestRateRemainingTerm" xlink:to="lab_trtn_DebtPercentageInterestRateRemainingTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_c630d8eb-9c6f-4cae-9e08-2a064c3ad484_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents Disclosure</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_6cc92e89-3a72-4ce6-b475-35b2557b3c9b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockRetiredCostMethodAmount_4e19e969-7888-446a-829f-30aee4016b34_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cancellation of Treasury Stock</link:label>
    <link:label id="lab_us-gaap_TreasuryStockRetiredCostMethodAmount_label_en-US" xlink:label="lab_us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Retired, Cost Method, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockRetiredCostMethodAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:to="lab_us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_12d86f25-9665-4391-a07d-3cf5833b00be_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MajorPropertyClassDomain_6776830a-8338-4a82-9159-5b11e88431f9_terseLabel_en-US" xlink:label="lab_us-gaap_MajorPropertyClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Major Property Class [Domain]</link:label>
    <link:label id="lab_us-gaap_MajorPropertyClassDomain_label_en-US" xlink:label="lab_us-gaap_MajorPropertyClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Major Property Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MajorPropertyClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MajorPropertyClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MajorPropertyClassDomain" xlink:to="lab_us-gaap_MajorPropertyClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableMember_450632eb-1d73-4790-b2f2-899c5a73d261_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableMember_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableMember" xlink:to="lab_us-gaap_AccountsReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorNetInvestmentInFinanceLease_05027812-8027-4be7-8955-5e447117f5f9_terseLabel_en-US" xlink:label="lab_trtn_LessorNetInvestmentInFinanceLease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment in finance leases</link:label>
    <link:label id="lab_trtn_LessorNetInvestmentInFinanceLease_ad6bc0e2-a410-4770-aa01-487563a538e6_totalLabel_en-US" xlink:label="lab_trtn_LessorNetInvestmentInFinanceLease" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment in finance leases</link:label>
    <link:label id="lab_trtn_LessorNetInvestmentInFinanceLease_label_en-US" xlink:label="lab_trtn_LessorNetInvestmentInFinanceLease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Net Investment In Finance Lease</link:label>
    <link:label id="lab_trtn_LessorNetInvestmentInFinanceLease_documentation_en-US" xlink:label="lab_trtn_LessorNetInvestmentInFinanceLease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Net Investment In Finance Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorNetInvestmentInFinanceLease" xlink:href="trtn-20241231.xsd#trtn_LessorNetInvestmentInFinanceLease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorNetInvestmentInFinanceLease" xlink:to="lab_trtn_LessorNetInvestmentInFinanceLease" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_f903bf52-85cf-4e74-8859-86812cedfa2e_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_eec32fba-7d8e-43a6-a545-bf24c6243064_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of (gain) loss on derivative instruments designated as cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_c4865286-e5f3-49fe-b8a2-36fbac8eed55_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.875% Series D Cumulative Redeemable Perpetual Preference Shares</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesDPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SeriesDPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesDPreferredStockMember" xlink:to="lab_us-gaap_SeriesDPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive_24a4fd4b-b655-41d2-80e5-ced5db65500f_terseLabel_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive_label_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Five</link:label>
    <link:label id="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive_documentation_en-US" xlink:label="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Recognized, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:href="trtn-20241231.xsd#trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:to="lab_trtn_LessorOperatingLeasePaymentToBeReceivedRecognizedYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_5a1551b4-1bbd-4ec4-bcc7-1d7c365f30d2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_1b6b704a-18f4-4f8f-91b7-364f0786e8fc_terseLabel_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_label_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NameOfMajorCustomerDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_NameOfMajorCustomerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NameOfMajorCustomerDomain" xlink:to="lab_srt_NameOfMajorCustomerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_6e491290-bd41-4825-b682-2a3173557f16_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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