Change child's last name?

While I was pregnant things between my child's father and I started becoming pretty sour, but we both agreed that we could be great parents and give our child his last name. We decided to move in and try to work things and suddenly he became like Dr. Jekyll and Mr. Hyde! He became such a dead beat, he doesn't want to work, he thinks that his SSI check from his accident is going to support our child. He's always in and out of jail because he says I push him to go out there and make money and winds up getting himself into something. I tell him to get an honest living job! Even if its Burger King who cares, something is better than nothing. I'm just so fed up with his laziness, and he doesn't even seem to care about himself he doesn't even like to bathe! I just feel him being a negative influence and I don't want our child to grow up with his last name. He say's he'll be in the picture but who knows one day he ups and leaves. I don't feel like our child should have his last name for the sake of how he is. However he won't give me permission to change but he's an illiterate who can't even give me a written consent as well. What can I do in a case like this? Thank you all very much!