Parent rights?

Megan
Ok so I'm almost 10 weeks pregnant and originally the father said he wanted nothing to do with the kid so I was going to give it my last name and I wasn't going to put the father on the birth certificate well now he is saying he wants the kid to have his last name but I'm still not putting him on the birth certificate but if I do give my kid his last name does that give him rights to fight for custody of the kid and take him/her from me?