Piping in to say “the Jenova War” is 100% not what the common folk would logically call it. In the OG, even those oppressed by Shinra bought the line that AVALANCHE was responsible for Sector 7, Meteor, and Weapon. Most people in FFVII’s world are fast asleep, and wouldn’t question what they’re told. Even if the WRO released a press statement exonerating AVALANCHE, and people were able to be convinced by it, they would still probably call the events of the OG “The AVALANCHE War” ———— if they called it a war at all. Three city bombings, a handful of kaiju attacks, and a near miss by Meteor doesn’t sound like a war. They don’t even seem like connected events.
Furthermore, if the WRO dished that there exists at least one hostile eldritch horror from space who can read minds, shapeshift, and eat the souls of the dead, I imagine that would hurt the credibility of their assertion that the terrorists were the good guys all along. And if people believed it, it would cause mass panic. If the WRO did that, they are more foolish than I originally thought.
Even if people bought the whole story, weren’t freaked out by it, and “word spread” I find it extremely implausible that they would a) call it a war b) name it “the Jenova War” instead of “the AVALANCHE War” or “The Meteor Crisis” or something that common folk would actually be able to point to and say “oh yeah that.”