Hmm, I think a play on the theme of "Fairy Tale" should be utilized for the name, though we should try to avoid using too many puns, as long fairy tales have a tendency to dragon...
More seriously regarding name suggestions for "Fairy Battle", I think the name suggestions should keep in mind that the song is for "Non-hostile" creatures seeking random items instead of blood and death, so maybe something like "Supernatural Conflict Resolution", or "Wiffle Bat Wonderland", or "Greedy Critters Seek Gift Giving Main Character's" should be used.