Quoted By:
The three characters are "the same" and her name is Blue (although her actual canon name should actually be Green)
This was because gen 1 didn't have a female counterpart, and therefore your rival got the counter version name of the game instead of the female counterpart, which at the time were Pokemon Red and Green, but later on Pokemon Green was replaced with Pokemon Blue because of glitches.
That's why the remakes are Fire red and Green Leaf instead of Water Blue.
Leaf doesn't fit her, because otherwise Red's name as well would be 'Fire' in the remakes, but he's the same character Red from gen 1. So her name should be "Green" instead of your rival's. And is probably she is named Green in LGPE.
I think this was because Pokemon didn't want to canonize her in the games, because Blue's first appearance was in Pokemon Special manga.
