If you efiled then check the status of the return. If it was accepted see below. With an incorrect name it might not be accepted. If it is rejected you can just fix the return and file.
If the return was accepted and haven't told the social security administration about the name change, then you should (tell the SSA) but perhaps you can just let this year's 1040 be as you filed it. If you have told the SSA they may will tell the IRS (they will but who knows how long it takes).
In the past I would except there to be a lot of slack in the system and that all that really mattered was that your SSN is right. But these days will all sorts for fraud it could matter. And they might issue any refund in the wrong name. You might (or might not) have an issue with direct deposit of the refund or the check. Sometimes banks are very sensitive to names, sometimes they don't check unless someone complains. If you're not getting a refund (or applying it to next years taxes) it probably maters less.
If it your 1040 has been accepted then you do have to file an amended return. here are instructions on how to amend a return.
You have to printout and mail. Amended return processing now is rumored to be very slow so be patient.
https://ttlc.intuit.com/community/amending/help/how-to-amend-change-or-correct-a-return-you-already-...
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