Changing your name at social security office?

State of North Carolina requires marriage certificate, proof of identity (DL/ID) and proof of United States citizenship (birth certificate/immigration papers) IF they don't have this on record. I have the marriage certificate and driver's license but my birth certificate has been lost for 15 years, and I have never needed it since. I am currently working with the state of Virginia to get my birth certificate. What does it mean by on record? How could the social security office NOT know my social security number printed on my social security card (which has my full name that matches my NC driver's license) belongs to a U.S. citizen? I'm confused, how could they of ALL people not know who is a U.S. citizen or not? Don't they have a database that says my number was issued by the state of Minnesota in 1989 to a U.S. citizen? Or am I misreading this and the social security card will be sufficient?
Changing your name at social security office?
These rules change by the hour. Take all the documentation you can to the SS office.