My daughters father wants to see her but I'm scared he will try and keep her an not give her back to me. He isn't on her birth certificate an she doesn't have his last name either so legally, could he keep her from me or would that be kidnapping??

If there has been no order for custody or visitation then he has no rights. But all he needs to do is go to court, establish paternity and he will get some level of custody and visitation. But that also protects you.

He has no legal claim without going though court.

It may not be kidnapping, each state ( in the US) has its own laws, from parental interference to interference with custody.

You have no legal obligation to allow him to see the child, BUT.. with that said, if he goes to court for visits and proves you have not allowed him to see the child, it will hurt you in court and could allow him more vistation time than he may have gotten before.