I'm a bit of an oddball. I chose my name a long time ago, but not because of my gender. As such, despite the fact that my name is chosen and I'm really quite happy with it, it... technically still doesn't fit my gender. x3 I identify as androgyne, yet my name is Diane. Which, when I first started figuring out the gender thing, felt kind of odd-- I had become so attached to Diane as my name, yet now here I was finding myself no longer identifying as a girl.
The solution ended up being quite simple, though, after I settled down and reaccquainted myself with my identity: Instead of making my name fit society's conception of gender, I rearranged my own concerptions of names and genders to encompass who I clearly feel I am. If I want Diane to be androgynous, the gosh darn it, it IS androgynous. (Heck, I think if I identified as a guy, I would still hang onto my silly name.)
I could come up with some brilliant tale of how I chose my name and how it fits me as an androgyne and all that, but I'd just be making things up. The name "Diane" latched onto me during a roleplaying game with my brother in 6th grade-- heaven only knows how it, of all names, stuck. More or less, I created a character named Diane who, in all my 10-year-old ingenuity, I forgot to gave a personality, so she just became me over time. I'm an androgyne running around with a clearly female name that was derived from a preteen roleplaying faux pas... and I really wouldn't have it any other way.
(I alternatively go by Crow, which is more recently added and definitely androgynous. However, the only people who really seem to call me crow are my students/kids I work with. Most of the rest of the world seems to call me Diane or some derivative thereof. Really, either is fine by me. As long as people don't call me by my birth-name, I'm happy as a clam.)