I'm thinking schnapps.
Apart from being a very pretty mountain flower, "Enzianschnaps" is also a rather well-known Alpine specialty (made of... wait for it... Enzian). When you are offered some, people usually just drop the "-schnaps" part and ask something along the lines of "Fancy some Enzian?". Well, I've been to the Alps just a couple of weeks ago, so that's probably why...
I don't much care for the drink, but I like the flower and I like the word.
As a name, though, I don't know. I think it's definitely more "name-y" than Edelweiß/Edelweiss, but...