Would you use the same name as your cousin?

I come from a big family, my mom is one of 9 and my dad is one of 6. So I have lots of cousins. I love my family dearly but I live about 1000 miles away from most of them (a large group of them all live in the same state halfway across the country from me) so I don’t see them nearly as much as I’d like. Last week, finally, DH and I flew out to visit and introduce our 2 year old to all the family out there. For reference the last time we saw most of these family members was about 2.5 years ago at my grandmas funeral.

So one of my cousins is also pregnant (funny enough our daughters are less than 3 weeks apart!), she’s due a little over 1 month after me. So we got to talking about names and come to find that we both have chosen the same girl name as our top choice. We were surprised because it’s not a super common name (even in Mexico). The other big factor is that neither me nor my cousin are planning to find out the sex of our babies. So it’s possible that one or both of us will have a boy and it’s a moot point but until the babies are born we won’t know.

Since I’m the one who’s likely to have the baby first I’m really the one who’s going to have to decide if I use the name first or not (assuming it’s a girl). If I do, it might make my cousin feel like she can’t use the name. If I don’t use it and she decides to use a different name anyway or if her baby is a boy then I’m going to kick myself for not using the name.

When we were talking we both were basically like “both kids could have the same name, right?” But it’s not like we had time to really consider either. So, would you use the same name that your cousin liked knowing that there are no guarantees the 2nd baby would be a girl and it’s likely that the kids would see each other only every few years at most?