If the father of my child is not on the birth certificate and the baby has my last name does he have any rights?

He has rights as long as you recognize him. However I think it is in your best interest to do so. <- that's an opinion only. If he signed anything like a recognition of parentage he has rights. In order for him to have rights paternity would have to be established on way or another.

If he can prove through paternity test that he's the father, he will always have rights unless the court denied him due to some danger.

As of now he does not have rights. But all he has to do is go to court and the judge will order a DNA test. When that comes back showing it is his kid then he will have rights and responsibilities toward his child such as visitation and support. The judge will also order that the because be changed to include his father on it.

He may get his rights anytime he wants, he has to prove he is the father with a DNA test, Then file for visits and the such in court. So not being on the birth certificate just means he has to prove he is the father to use his rights.