On your tax return you enter the name that is on your current Social Security card.
To update your TurboTax account information see this TurboTax support FAQ - https://ttlc.intuit.com/turbotax-support/en-us/help-article/account-status/update-turbotax-account-information/L0YoC0H31_US_en_US?uid=m8rutbdr