My son is 3.5 yrs old and the father is in his life we actually have joint custody but he is a worthless father. In the state of California can I change my sons last name to mine without consent of the father is he is not on the birth certificate. When my son was born we were not married and he refused to go and sign the birth certificate.

If the father is not on the birth certificate, then how does he have joint custody? To have joint custody means he has been determined by a court to be the legal father. As the legal father he would have to consent to any legal name change.