<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-02-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001487986</issuerCik>
        <issuerName>Hawaiian Telcom Holdco, Inc.</issuerName>
        <issuerTradingSymbol>HCOM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000947822</rptOwnerCik>
            <rptOwnerName>FEINBERG STEPHEN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CERBERUS CAPITAL MANAGEMENT, L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>299 PARK AVENUE - 22ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10171</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2011-02-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>150000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.40</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>986042</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By limited liability company</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2011-02-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>57000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.4754</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>929042</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By limited liability company</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">As of February 2, 2011, Cerberus Series Four Holdings, LLC holds 929,042 shares of common stock, par value $0.01 per share (the &quot;Common Stock&quot;), of Hawaiian Telcom Holdco, Inc. (the &quot;Company&quot;) and warrants to acquire 186,747 shares of Common Stock.  The 929,042 shares of Common Stock held by Cerberus Series Four Holdings, LLC includes 46,709 shares of Common Stock that Cerberus Series Four Holdings, LLC received in connection with the settlement of certain trades of senior secured bankruptcy claims, which claims pertained to the Company's outstanding senior secured debt issued under the Company's Amended and Restated Credit Agreement, dated as of June 1, 2007.  These trades were executed prior to the registration of the Common Stock under the Securities Exchange Act of 1934, as amended (the &quot;Act&quot;), and thus, the acquisition of the 46,709 shares of Common Stock is not subject to Section 16 of the Act and is being reported herein for informational purposes only.</footnote>
        <footnote id="F2">Stephen Feinberg, through one or more entities, possesses the sole power to vote and the sole power to direct the disposition of all securities of the Company held by Cerberus Series Four Holdings, LLC. Mr. Feinberg's interest in the securities reported herein is limited to the extent of his pecuniary interest in Cerberus Series IV Holdings, LLC, if any.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Stephen Feinberg</signatureName>
        <signatureDate>2011-02-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
