And none of Cygame's stuff is strictly alternate worlds of each other. In fact, if you count crossover events as canon, then they're completely separate copies of the characters, then. It's more just that Cygames likes to re-use character designs.
With that said, there's a very high likelihood that if her last name ever shows up it'll be the same, since that's basically what Cygames has done with the rest of their stuff. The character designs are almost identical, so an alias would make sense.