Upvote:3
I don't know anything about how the US State Department carries out interviews. It would be a good idea to have your marriage certificate, issued by the agency in the place where the marriage took place, that issues such certificates. If it isn't in English, I would obtain a translation into English. Check the State Department website to see if you can find any information about what rules the translation has to comply with.
In the US most states don't require a wife to go through any formalities to start using the husband's surname after the marriage, which is why just a marriage certificate is usually considered sufficient proof of the name change. It also isn't unusual for a woman to use the birth surname professionally, but the husband's surname socially. You might encounter more questions if it has been many years since your marriage. Let's hope the flexibility found in American society carries over into the State Department.
Having the marriage certificate and translation will be helpful for any extended stay in the US, not just the State Department interview.