I think it's a beautiful name. I instantly make the connection to the chamberlains but I don't think that's a reason not to use it. She was a beautiful baby from a beautiful family.

The due date/birthday date connection on top is a bit weird though TBH. It's a bit obsessive/stalkerish, as though you want your child's life to follow in the footsteps of the first Azaria. I know you don't of course, it just comes across as odd and if your baby IS born the same day I personally wouldn't be able to use it.