How can I remove his last name from my child’s birth certificate

My boyfriend and I have officially broken up when my child is only a month old. We have not lived together. He hasn’t given me any money to help with the baby. Has seen him only a few days a week since he has been born and his sister told me today he told them throughout my whole pregnancy he doubted it was his. This breaks my heart because this man knows it’s his child, and he never expressed these thoughts to me. So if he tells his family that, doesn’t help me financially, and doesn’t want to be a full time dad than he doesn’t deserve to have a child with his last name. I need advice. Do any of you have any legal knowledge of how to go about this or have been through the same thing?

I’m not wanting to remove his last name because we broke up I’m wanting to do it because he has made it more than obvious he wants no responsibility as a father. I’m not depriving my child of a father, he has deprived himself of a son! Our child is a month old and this man hasn’t bought him anything but one package of diapers. I paid all of the hospital bills for maternity care and am now making payments for delivery/ csection on my own. Even with my blue cross insurance its still an arm and a leg. He isn’t a child. He is 40 damn years old. He doesn’t deserve to have a child walking around this world with his name when he doesn’t give a dan about him.