My question involves paternity law for the State of: Texas

This is my situation and I am in need of some help BAD. I was with my ex bf and when I found out I was pregnant, he and his family treated me like crap. I had not seen, spoken, or known about him since the day I left our home. I recently bumped into him and he decided that he wants to be in our sons life. He has not been there finacially or emotionally for us. I am already 7 months preg and in 2 months he will be here.I dont want him having anything to do with our son. I was not going to ask for child support nor give him his last name. He decided to tell me that he is going to fight for him. If i dont ask for any type of cs nor give him his last name, does he still have a right to him? He brings nothing good. Neither does his family