Well this whole campaign isn't canon, and it would make sense for ST:R to name it the Legion, if it was involved with their campaign, because it's one of the closest things we have to fanon right now.
If they didn't, I'd understand, but unless they had a purpose for not calling it the Legion, I'd be downright confused as to why.
So the Legion is fighting the Shivans in the midst of the Great War why? I mean, I think they started the war somehow, but you'd think they'd let the GTA take the brunt of the attack once the Shivans actually attacked...
Or was it the Shivans who attacked the GTI? Was something the GTI doing the motivation for the Shivans to attack? In that case why did they attack the Vasudans and the GTA?