When Trump got elected I went to court and changed my name and changed my birth certificate.. it took about 6 months and the birth certificate was very slow in arriving. It doesn't actually change your original birth certificate but adds a page 2 indicating the change.

If you are a person who has changed their name there is no guarantee a marriage license will work. If you are going to do this now is the time to start it. Just get certified copies of your original that you can use in case you get your freedom back.