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Introducing the new butthurt copypasta to smack sense into people: Prepare to get mad.
>US Pokemon games - Gen I [RBY]
The boy is Red.
The rival is Blue.
The girl character seen in concept art with Red and Blue is unnamed.
>JP Pokemon games - Gen I [RGBY]
The boy is Red.
The rival is Green.
The girl character seen in concept art with Red and Green is unnamed.
>US Pokemon Adventures
The boy is Red.
The rival is Blue.
The girl is Green, her initial appearance was based off the unnamed girl mentioned above. When FRLG came out, her appearance was changed to match that of the female playable character.
>JP Pokemon Special
The boy is Red.
The rival is Green.
The girl is Blue, the details with above stay the same.
>US Pokemon games - Gen III [FRLG]
The boy is Red.
The rival is Blue.
The girl has no official name, but dummy trainer data lists her as Leaf. Although the same data lists Blue as "Terry", this is the most commonly accepted "name". Because she looks similar to the manga character and the unnamed girl in Gen I concept art, some people refer to her as such.
>JP Pokemon games - Gen III [FRLG]
The boy is Red.
The rival is Green.
The girl again has no official name.
The Gen III details are consistent with the rival's appearance in Heartgold and Soulsilver.