The facts..... XIII and VS XIII were announced at the same time, under the Fabula Nova Crystallis moniker, and known to be linked in some mysterious way. If the two take place in the same world, they clearly are in vastly different eras in time.
XIII-2 involves time travel.
I think all things considered, it's highly likely XII-2 acts as a transition/link between the two games, and this caused them to consider just renaming VS as XIII-3. I don't take this registration as a confirmation of a name change, only that they are considering it.
And I'm completely ruling out XII-3 being an actual new game. To me that's just way too redonkadonk.