I don't think that you should back down from using a cool name even if it is becoming more popular by the second. I mean, I wouldn't use Katniss or anything like that, but I think Aurelia, despite becoming more popular, is still not that well known, and is a very beautiful name. Just because a whole lot of people like it doesn't mean you shouldn't use it. It's still very unusual, and I think the popularity of the name shouldn't effect your use of it if you think it is a fitting name for your character.
I know that, but it's awfully close to Amelia, and that's a girl I know. I'd rather not name her anything close to that... Oh, what am I to do??!
Where are you looking when you're saying it's becoming "popular"? It might be somewhat popular here on berry lists but it's nowhere near being popular in real life.
Aurelia is a beautiful name and gets more attention on Nameberry than on real people's short lists. I know two Ariels, an Arielle, and an Aprielle, but I've never met any one named Aurelia. I don't expect this name will ever hit the top 100 in the US, unless you write the next cult-following teen fiction series that influences the next generation of parents.