I know someone whose kids have their father's last name, and the only issue she ever said she had is some times she would have to prove she was the mother by showing their birth certificate (more often the other people).
I’d double barrel the surname if you’re not married. Just if you do split up (I know it’s not nice to think about) and you want to take baby abroad etc he could stop you as the baby doesn’t have the same surname.
@Chloé Collier even with the birth certificate?
My partner and I hyphenated our son’s last name so it has my last name and his last name. That could always be another option if you wanted.