CLARIFICATION TIME. Prepare to get buttmad

>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 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 this is the same data that lists the rival as "Terry", it is the most commonly accepted "name". That said,

since she looks similar to the manga character and the unnamed girl in Gen I concept art, some people refer to her as such, which only makes the situation more convoluted.

>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.

Any questions?