My boyfriend and I just had a baby. I did not add his name to the birth certificate and he wants me to add him to it giving our child my last name and his last name. Can he come take her from me anytime he wants if I do this? We both live in Florida he lives in a different part of Florida but I just want to make sure I am safe if I put his name on it

You get his name added and go to court and file for a custody agreement order from the Judge then stick to that.

Amending the name on the birth certificate should have no bearing upon your complete custody of the baby; it's just that he has 'equal' custody with you until you get an order from a court setting forth rights and obligations of custody, visitation, and support.