My fiance' lives here in Ohio with me. He has been trying to get his baby's mother to let him see his son and she refuses to let him be the dad he wants to be. Now she is telling him that she is going to change their sin's last name to her boyfriends last name. Mind you she has known him for two months. In the state of Florida would she be able to change their sons last name without his consent? If considered an abandoned parent, even though he is trying to be in his son's life... would she still be able to change their son's last name?

No, a name change cannot legally be done without both parents consent. It wouldn't be the first time someone lied to a court to get it done though.

If he is trying to see his son and its not working he needs to stop talking to the mother and start talking to the court where they will ORDER her to let him see his son.

Get a lawyer and file for paternity and whatever custody/visitation he wants.