How can I file for child abandonment against my ex. He is on my son's birth certificate but is not the biological father. I have the paternity test results to prove it. He says he is not signing anything to take his name off. What can I do to get his name off it and change my son's last name?

Are you asking about filing against him for Child Abandonment OR is your interest taking his name off the birth certificate OR do you want to legally change your child's last name?

How old is the child?

You are putting the cart before the horse. It appears that you are looking at making him pay child support so as to force him to admit that he is not the father and agree to changing the BC & child's name. But what do you hope to accomplish by that? Is there another father-candidate in the wings?