Well the barbarians are barbarians
They could be called the barbarians "in the north."
The green faction never got a name, however there is a reasonable theory that green is supposed to be affiliated with Moorbach. In TSK, Moorbach is the city to raze in TSK 5, who uses the purple banner. Now, all lines of mission "script/code" for original KaM has to start with an exclamation point, for example: !SET_PLAYER_COLOR (or something, I can't remember the exact syntax!). Anyway, in TSK 5, there is a line of code for the "purple" player that is supposed to set his color to green. However, the exclamation point is missing, so the code doesn't do anything. If this was done by oversight or they just ended up going with the purple color...who knows?
Now you might ask if TSK 5 purple is supposed to be green, then what is purple doing in later missions, too? It would be unlikely that they kept using purple after an inital mistake, right? Perhaps, but if you look at the purple "leader" who is slain in the video following the completion of TSK 12, you will see a leader who is wearing a "Viking helmet." He also looks very barbaric. Johann von Moorbach was a scholar, so this doesn't seem to fit his character well. It was proposed that the purple player here is supposed to be affiliated with the barbarian chieftains...meh idk.
TL;DR: The green faction doesn't have a name. Tony (a very inactive member of the forum!) made some walkthroughs where he referred to the green faction as the "Imperial Guard" or something like that, in reference to the green faction appearing around the same time as Prince Lothar.
The player (red) is leading the armies of King Karolus. He is supposed to be "the player" who is referred to as "the new herald of the king."
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