I specifically love Greek mythology. I know the most about this particular type, and I've been to Greece and loved it.
Artemis is my favorite name. It's perfect to me. I often joke around with my mother and say "the first kid I pop out -- if I pop out any -- I will name Artemis." It works, you see, because of the whole double gender thing. Artemis because of the goddess or Artemis 'cause it sounds like a guy's name.
Echo is a guilty pleasure, but other kids would probably make fun of her (yes, a her. There was a whole debate on it in the comments.) by saying "ECHO...ECHo...ECho...Echo...echo."
Eurydice
Endymion
Selene
Ajax
Cadmus
Yeah, there's many others but I can't particularly remember them all. It's been a while since I last "studied" them.