Fiancé’s last name - Will naming baby be a problem??

kyrie • 22 || CO || capricorn || bartender || lily zephryn 2/3/18

So, my fiancé’s last name is legally Ebben, that is the last name of his step dad that raised him. But he was a terrible step dad, sold all of his stuff when he was in high school, doesn’t speak to him anymore, etc. His biological father didn’t come into his life at all until he was 15. He never knew even knew about him. But his last name is Burke. And that’s the last name he wants to have legally and for our daughter due in six weeks, and me eventually whenever we get married. So my last name is currently my maiden name, Larreau. So I’m wondering, if he doesn’t get his name changed before baby is born, is she gonna have to be either Ebben or Larreau? Or can we name her Burke and then get our shit together and both of us change our name to Burke also so we can have the family name we want ??