Baby's last name?

I don't know where to ask this. Baby's father and I are not together, and for numerous reasons will not be getting back together. He wants to be involved in baby's life, and I see no issue with that. We plan to keep things civil for baby's good. However, I see no need to give baby his last name? In my reasoning, if baby is going to live with me, I would like matching names in our household. I know my mother and I have different last names, and it gave me numerous amount of little problems. I had to get almost everything notarized to prove she was my mother. Would the hospital put my last name regardless of his opinion?