Which Last Name Should We Give Our Baby Girl - Needed for Birth Certificate!

Hey ya'll, wife just gave birth to a beautiful baby girl, and when the nurses gave us the birth certificate, we ran into a problem. I need your help on which last name we should go with!

My wife and I both agreed when we found out we were having a girl, that we'd go with the Eileen. Coincidentally, both of our respective "favorite" grand mammy's (when we were kids) were named Eileen, so we felt it was a perfect choice, didn't think twice.

When I put Eileen down on the birth certificate, one of the nurses started laughing. We weren't sure why, but then she said "Mr. Dover, you're not seriously going to name your baby Eileen, right?" I get where it could cause our daughter to get made fun of a little bit, but it's certainly not as bad as some of the other names I've seen, or at least I didn't think it was until this nurse immediately started picking on it after hearing the name. My wife didn't take my last name, so I said "why don't we give her your last name?" and the nurse looked at my wife's name on the patient board and laughed even harder. She even called in some of the other nurses to share the laugh. We were confused, but it was also embarrassing!

I don't really see a problem with the name. I get that Eileen Dover is a bit funny, but i don't see any issue with the name Eileen Eulich. Which do we go with? Would it be better if we hyphenate? Eileen Eulich-Dover or Eileen Dover-Eulich?

(no sauce, this is a satire post)