When I had my daughter back in December my divorce to my now ex husband wasn't final. So in the state of Tennessee if your divorce isn't final 300 days before birth my ex husband is legally her father and she had to have his last name on her birth certificate. However on her birth certificate under father name is blank. If her biological father and I marry how would I go about getting her last name changed and his name put on her birth certificate

Who is the legal father of the child at this time? It sounds like your ex husband is so your going to have to get his permission for an adoption and at that time a name change.