We were very selective about who we shared name choices with prior to our last daughter being born. That being said, I did share with a few friends and online, because I wanted to get some reactions from people whose opinions I trusted and valued (in the case of my friends) and also from people who had no real stock in trying to make me happy (people online). I wanted to get some honest reactions to the names, as the kid will be the one to live with it, not me. If one of my friends didn't like a name, but it was just a matter of preference, it didn't concern me much. If a lot of people had had a negative reaction to a name though, I would have assumed that that's going to be the general reaction and either stuck the name in the middle (if it had a lot of meaning) or chucked it altogether.
I do agree that once your kid is named that it becomes their name, but I think Edelweiss will be a hard one for a kid to live with in the US. And for people who know her the name will fit, but there will be people who will see the name on paper before they meet her who might have preconceptions because of it. Likely she will end up with a nickname, like Edie or Adela or something along those lines. Especially when she's younger and her friends have trouble pronouncing it. If you used a name like Adela, and said she was named after the flower, or put Edelweiss in the middle, would it still hold as much meaning to you?