In NJ, my friends ex wife wants to change their 2 children's last name. He pays child support. Does she have that legal right do to so? I don't think so without his permission correct?

A birth certificate is a legal document, so it can only be changed by court order. Both parents would have to consent to the change for a court to issue the order.

However, a person can use any name they want as long as there is no intent to defraud and as long as they present their legal name when required.