Is he going to be listed on the birth certificate? I don't know if it's a "right" or not. I do know that when my granddaughter was born, she initially had our daughters last name and he wasn't listed. But after, they agreed and had to get an affidavit of paternity, and have it registered at the courthouse to have her name changed. I believe if the parents are not married both your son and the mother have to sign that.
Edit: I know you say that he will be responsible from the beginning, I strongly suggest, even though it's not required, getting court ordered visitation rights and a child support order. Too many things can happen and if he has that at least his rights are protected as well as hers. 4951