Her biological father is not on the birth certificate and has never paid child support or anything.. We live in Texas and I just don't want her to have a different last name from everybody else. How easy would it be for my fiancé to adopt her legally?

Not hard at all, You get married and be married for one year. You hire an attorney to draw up the adoption paper work. You get the bio father to sign over his rights ( part of the paper work the attorney will draw up) and file it in court.