If my baby has father last name and were not together (he moved out state) :) who gets to claim child for tax time? Btw My baby is four days old, what would be different if I changed his last name to mine? I don't think it would be right for the dad to when I take care of the baby. I have healthcare and stamps, I called to put my baby on healthcare and they wanted the dad so that child support can go after, he has kids already with his last name. I didn't ask for child support to be involved but would they stop my benefits and why?