[Opinions] I think Anya could work
I agree with you that the logic is a bit screwey, but I also agree with Dragon_Clarinet that you can't really compare the end result with Eolh. Its kind of like saying that Hturt should be workable as a fn because Nevaeh does- the fact is (whether we name nerds like it or not) that Nevaeh has a namey sound and is therefore usable.
People come up with nicknames in all sorts of random ways. My brother gets called Mippee or Mip (because apparently we feel the need to shorten the nn as well) because his initials are MPE. It isn't the best logic or the nickname that makes the most sense but it does work. *shrugs*
P.S. I am generally of the opinion that nicknames are fair game. I often find that ones you assume will stick or that you really want to stick just don't and then unexpected ones just seem natural. They don't really have to make a whole lot of sense.