I'm not too sure! I'd assume they're just Red and Blue, yeah. Although, the are games and we know that the games do not follow the anime or the manga all that accurately (if at all). With that in mind, they might perhaps just have regular names like we all do.
I've got to say though, that despite popular belief that Pokemon Battle Revolution was a really bad game, I actually loved it. Although it did make me furious in the later stages when I kept getting smashed by trainers in the final championship.