Note that if a USC wife wanted to change her last name to match the last name her husband had at the time of the marriage, she normally would not need a separate court process. She could just start using the new name, and the marriage certificate would serve as evidence of the name change.
But it's a different situation if the husband is changing his name after getting married, and she wants to change to that new name. In that case, the marriage certificate would not be sufficient; a separate court process would be required.