That depend on the amount of information.
The characters aren't necessarily the same (As they never are in Pokémon). But even when we are dealing with literal versions of different universes, some are still in the same profile. Cyrus is a good example, our current profile includes not only the one from the D/P games, but also Pt and the US/UM games, all from different universes. Yet the one from Masters is also from a different universe from the one that Masters takes place. I think that Masters does not add enough information for most characters than a new Core Game, and if is supposed to really be taken place in the world of the characters of the games (That by itself is already a multiverse), then a key for "Masters" should be enough.
Yet I don't think that different keys of different profiles have any different meaning other than being in a different page or not. So isn't really a question that I can answer as it does not deal with the setting/worldview, that is the thing that I know of. People who works on the profiles themselves might know the better way to do that.