Custody and baby last name?

My boyfriend and I broke up about a week ago. Before that we had been saying the baby will have his last name when she is born. Now, im worried that if i give her his last name, he will be able to cause all types of custody problems for me. I want sole custody of her and he was fine with that before. Also i told him i was moving to California nd he was fine with that too. But now im scared he will try to fight me. So im wondering what i should do. Please help and please NO RUDE COMMENTS.