No, you do not need to change your former name to your married name on your social security card to file jointly. However, if you haven't changed your name with the Social Security Administration (SSA), you will need to show your former name on the tax return instead of your married name to avoid delays. It is important to ensure that both your name and Social Security Number (SSN) on the tax return agree with your social security card to prevent any delays in processing your return and issuing any refunds. If you decide to change your name on your social security card due to marriage, you can visit the Social Security Administration's website or call them at 800-772-1213 (TTY 800-325-0778) for more information.
Sources:
Publication 1380
Publication 501 (2023)
Rev. Proc. 92-32