You know, if there is some big alien space empire out there, then our planet and moon might have names based upon THEIR language and naming system. And since they would out-number us (and be more technically advanced), that means they get to pick the name. So, stay tuned.
H.G. Wells wrote a book in which two men go to "The Moon" and encounter Selenites. Even earlier, Jules Verne discussed the (past) existence of Selenites. According to Wikipedia, Verne's novels "inspired the first science fiction film, Le Voyage dans la Lune, made in 1902 by Georges Méliès (English title: A Trip to the Moon)." That movie definitely has Selenites. But there are even earlier references to Selenites in scientific (!) and classical literature, according to this website:
http://www.daviddarling.info/encyclo.../Moonlife.html
So, I vote for Selene. Now all you Greek-speaking people can write in and complain that selene is just the Greek word for moon.