Update:
Went to the SS Office today. Prior to the visit, I filled out the Request SS card app which allows for a new card to be requested with updated info.

I met with the rep, gave her my application, current EAD (which does not show my new name), and my marriage certificate (showing my new name). She asked me a few questions, mainly verifying the info in the app. She processed what she needed on the computer and gave me a receipt with my new name reflected on it. She said I should get my new card within 10 days. Took less than 10 minutes.

A huge headache avoided! Thanks for your input, DBR and JJ!