How would I get my daughters name changed and birth certificate signed by my fiancé who is incarcerated? I'm trying to get her last name changed to his

You get signed consent from the father. What State?

Some prisons/jails have a notary available to inmates/prisoners. Others do not and will not allow legal documents to be signed while the person is incarcerated. He doesn't sign the new birth certificate. Depending on the State he signs an Affidavit of some sort.

Has DNA been done?

Is he the father?

If not, you either need to do a formal name change (through the courts) or you need to get married, be married for a year, get permission from the biological father, and go through the courts to have your HUSBAND adopt.

If he is the father, you still need to go through the court, but generally just need to present proof that both parents are in favor of the name change.