It was proven by DNA that my ex boyfriend was not my Child's father. I do know who the father is and am getting help so have to provide child support office with the fathers information. He wants nothing to do with my son. Does he have to take me ti court if he changes his mind or will he automatically have rights? Does he go on the birth certificate? I had plans to move to another state will there be a problem with my doing so?

Ok, he has "rights" he just can not enforce them without a court order. If there is not a child custody order in place you are free to move. He may at any time go to court to ask for visits, joint custody and other rights if he wishes.