Well, you could get around this by just keeping a real asian name. I for one have no European descended name, and I'm sure there's some AA females out there who also don't have Eurodescended names...I mean, if you're not really descended from Europeans it's kinda silly to go and change your name to one in my opinion. The "American" versions of those european names have been tweaked to be spelled differently over time themselves, so why not just spell an Asian descended name with an Americanized spelling? Makes a lot more sense versus naming your daughter Catherine after some ancient European royal lady or something(please note that I haven't actually traced where Catherine comes from but I'm thinking of Catherine the Great).
When I was younger I disliked being teased for having an asian name that nobody could pronounce(at the time people were still jackasses apparently), but as time has passed not only have people learned to pronounce my name very quickly(teachers often got it on the first try, particularly college professors are very adept at this), but suddenly it was awesome to have a unique name, and not be one of 100 people named John on campus. Instead of people referring to me as Laura2(I only say Laura2 because my friends actually refer to a girl as Laura2 to avoid confusing her with Laura1 lol), they can just say my name. Incidentally Laura1 is asian fwiw(although I believe she might have been adopted by white people so the naming thing might not be valid here).
At any rate, I think people should be proud of their past and their names should reflect that instead of being some weird attempt to fit in by grabbing "western" names with no real significance to them. No offense to any Asian people with Eurodescended names, but that's just how I feel. I think most of the people who stuck with a non-Euro descended name are probably prouder of their past and their family history in Asia. Plus it has long been written what my name should be like, and it would be a terrible break to tradition to forget. Most of my cousins in the US have Americanized names though, but on the upside they do have Chinese names too, so at least an attempt is made not to forget what name your ancestors would have wanted.
On a side note, if you think it's some weird spiritual thing about what your ancestors would have wanted, it's not lol. There's actually a naming system for many Chinese families where each generation is supposed to have names laid out in a specific way. I think the way also manages by family as to what exactly has been predetermined, but there's obviously flexibility so that not everybody in the family has the same name. Too complicated to explain quickly without explaining how the chinese language first so I'm just gonna leave it at that =p So yes my name was partially determined thousands of years ago by my ancestors.