What a unique and pretty middle name. My best friend in elementary school had it as a middle name, and so did her mother. It was a family tradition, so that each little girl could think of herself as a fairy.
I find this name wonderfully elegant- mainly because it is my nickname; my real name is Fahara: though I don't quite know where my mom pulled it from. Fae is what most call me and I stick to that like glue.
Personally, I prefer this spelling over all the others. When you take out the "y" and just have "Fae" it seems so much more magical.
Note: Currently, my favorite name is Fae (hopefully this doesn't change anytime soon). However, I used to want to be "different" and have the spelling be Fey--until I read that in British slang/idiomatic language (particularly Scottish), to say that something was "fey" meant that it was doomed to die. So I had to change the spelling! :-)