Name advice - re-use in the family

Hi ladies! After your thoughts on something. My wife posted on mumsnet about this and got some pretty weird responses because they’re all a bit berserk over there, hoping for some more rational thoughts over here!

So basically, we like gender neutral names (as a lot of you guys seem to as well!). Our 2 year old daughter has one (with a feminine middle name), and we’re looking to take the same approach with daughter #2 when she gets here.

One of the names we like is already in use in our family - a cousin we don’t see very often and aren’t particularly close to has a 9 year old son by the same name. Do you think it’s ok to re-use that name for our daughter? We would probably ask him first to check he’s ok with it, but I think it would be a bit weird for him to object?

Thoughts gratefully received!

(The mumsnet chat descended into a critique of the name itself, which isn’t the point of this, so I’m keeping it out of my question). Thanks!