In the hospital and need to pick a name quick

Update: We ended up going with Daphne Eleanor as first and middle name. Thank you everyone for sharing your experiences, we were able to get a bit more breathing room from the registration office which helped us spend time with our little love before jumping straight into a name. Her brothers are very excited to meet her and it looks like she may be coming home as early as Friday!

Baby came earlier than expected (34 weeks) and we had her yesterday on Valentine’s Day. I already have the birth certificate lady coming to our room every few hours asking for a name which is stressing me out since I haven’t had the chance to hold my baby as she is in NICU while I am being treated for complications.

We have 2 toddlers, Jack and Rhys. Our top list of names so far:

Evelyn

Daphne

Olivia

Eleanor

I’m concerned about the popularity of Olivia although I’ve loved it for awhile. I don’t want her to be one of 4 Olivia’s in class. For context, we live in Florida but split a lot of time in the UK. Thoughts or other suggestions?