As well as agreeing to in the the Answer to my petition does not demonstrate that she is not allowing my son to have my last name from birth as a means of hurting me?
You're not seeming to understand that the child's last name is going to be decided by the courts based on the best interests of the child, not based on you being pissed at Mom.

How is it in the CHILD'S best interest to bear your name? THAT is what you have to convince the courts of.