In the state of West Virginia, can you change the child's last name to the fathers name if the father has primary legal sole custody of the child? Without the consent of the mother? Due to abuse and neglect the mother lost rights as primary guardian of the child and has only supervised visits...

You would still have to seek permission for a name change.

Agree, the other bio parent will have to give permission. Or she would have to be served and refuse and you try to get the court to order it anyway. ( not as likely)