Fathers Rights to Last Name of Child in New York

My question involves paternity law for the State of: New York

At the time of my son's birth, there was a question of whether or not I was the biological father. His mother and I are not married. A month after he was born, I went for a paternity test and the results stated that I am his father. We have since gone to family court to establish legal paternity in the eyes of the state. My son's mother got his new birth certificate in the mail and it now has my name listed as the father. Along with the birth certificate came a form to change his last name. Currently his last name is his mother's but I would like to change it to mine or at least a hyphenated name of his mother's and mine. His mother is refusing. I am very active in his life - he is with me every week - and I pay child support. Do I have any legal rights in New York State to his last name? I am prepared to petition the courts if need be, but I would like to know if I have any rights here. Are there any legal precedents that I can look into?

You'll need to petition the court to change the child's name if you want and let the judge decide what the child's name will be. You have no inherent rights as to what the child's last name will be. That only comes along with being a husband.

Thanks for your reply. Is there any case law or legal precedent that I can refer to or read up on for this situation?