It may surprise some people, but the Constitution does allow for such an action. It requires the approval of Congress, however, and that will never happen. It has been a long time since a state was split, notably West Virginia and Kentucky separating from Virginia. Of course, the Civil War had a lot to do with that.
There have been numerous attempts to split California in half, west to east, but this is the first time I've seen a proposition to divide the sate into three parts. I would not be surprised if the measure passed on the ballot, considering the very different social structures of different parts of the state. And those of us who live in the small area which would retain the name California really don't have a lot of respect for those in the north and south.
It won't happen, of course; there's no way the federal government would approve it. But it does present some interesting matters to consider.