If you have excess Social Security tax withheld on Schedule 3 line 10 you will have to amend the tax return. If you don't amend it, you will get a notice from the IRS telling you that you are not entitled to that credit. You did not really have excess Social Security tax withheld. It only appeared as if you did because your spouse's W-2 looked like it was yours. You will have to repay the incorrect credit that you received.

If you don't have any amount on Schedule 3 line 10, or you don't have Schedule 3 in your tax return at all, there is probably no need to amend.

If you do have to amend your tax return, don't do it until your original tax return has been accepted and processed, and you have received the original refund.

When you start your 2021 tax return next year, and transfer information from your 2020 tax return, that mistake is going to get transferred to 2021. Your spouse's W-2 will transfer as yours. Be sure to correct it on your 2021 tax return.