So the father of my son who is 13 months ol is taking me to court to be added on the birth certificate and whats to change his name as well. Can they make me even if he gave me sole custody when he was 2 months old?
call a lawyer. Now. Most will do free consultations. There are some interesting situations where if you knew that he was the father, and refused to put his name on the birth certificate you could be in lots of trouble.
I'd get some free consults with attorneys. I don't believe anyone can make you change your child's last name even if you put the father's name on the birth certificate. Not every culture uses the dad's last name. That is a personal decision.
I'm no expert but my understanding is this: he can certainly take legal action, get on the birth cert, petition for visitation (and he'll get some sort of visitation if he has his shit together), but he can't do anything about the last name!!!
Is the custody agreement in writing from a court or did he just abandon you and your child? If he abandoned the two of you then I think you need to get a lawyer and ask for phased in visitation with frequent visits at your home for several weeks then short frequent visits on his own before moving to the basic visitation recommendations that your state has laid out (or if your state doesn't have them the most basic plan your lawyer thinks you can get through). You also need to press for child support dating back to the time of your child's birth and half of any medical costs incurred from the birth and after. If the custody agreement was in writing he can still go back to ask that it be modified.