I have a son and I gave him the fathers last name ! And my son is 2 moths old and the dad sing the brith c . But don't pay child support can I change my sons last name to mine?

No, you can not simply change his name. If the father agrees then it can be done but if he does not want the name changed then you can't just change it. Do you have an order for support? That would be the first step in getting support payments. If you do have an order then you will have to go back to court to have the order enforced.