Question about changing childs name...?

Can I change my son's middle name without his "fathers" permission? His dad has nothing to do with him. He has given me $15 total, and my son just had his first birthday. He is not on my son's birth certificate, and my son doesn't have his last name. If I were to show proof that he has nothing to do with my son, do I still need his permission?? (I actually have a text saying that he wants nothing to do with him.)