I don't think the name 'Gantz' matters at all. Someone that used to belong to a previous Tokyo Team just gave it it's nickname and Nishi continued to use it. That's all. The Osakans never called it Gantz.
But I think this is a pretty fascinating development. I also think that the numbers the fat woman speaks are some sort of alien signal and that everything the guy and his organisation have done is just a game to them. They have no real clue what's going on either.