OP - you asked: 'is this really an issue???' and got a rather overwhelming response that yes, it is. It's not the end of the world, but it is an issue. People aren't, for the very most part, being bitchy; just answering your question. Are you surprised by the answers?
I honestly think you were being rather disingenuous to assume that this wouldn't bother most people.
If I were your SIL I wouldn't fall out with you over it, but I'll be honest, I'd be totally eye-rolling you behind closed doors and thinking it was all a bit petty/pathetic/cringey. You're the one who's going to come out of this the least-best, since you're going to look like the copy-cat, the one who couldn't even come up with an original name for a new family member.
I honestly don't mean these comments to come across harshly or bitchily, but a lot of people will have a, 'huh, odd choice' moment when they hear the name, and it's not going to be your DB/SIL that this reflects back on.
Aubergine - it's totally different. It's not as if your DB went out looking for someone with the same name as you; he met and fell in love with someone who happened to have the same name. The OP was obviously fully aware of her DN's name when she chose her DD's.