Still, if there is only one, there is no need for a name. Did you know that until his death, the Emperor of Japan is named simply, "the Emperor?" Only after death do they get named "Emperor Meiji" or "Showa" or whatever. Likewise the Moon and the Galaxy have no names. I suppose, in many languages Earth doesn't either, being called simply "the world."
But I can see fun overrules that argument. Therefore I suggest we henceforth call the moon "Princess Serenity."