Well, if 'December May' is a relatively unknown or a very specific reference, it could be a true story within a certain community or family. For example, it could be the name of an event that happened in December and involved someone named May. However, in general, just from the name alone, there's no way to be certain that it's a true story. It could also be an artistic name for a fictional piece, like a song or a short story.
It's hard to say. You'd have to look at the background and details of the story. Sometimes, even if it has elements of truth, it could still have fictional parts added for drama or entertainment.