I would actually recommend sticking to Fediverse to REDUCE the confusion that Mastodon has caused. If people referred to Mastodon as the Fediverse or even fediversetodon or something it may help. But calling it the Twitter alternative all the time has just said "screw twitter, it's mastodon now!" and that's where people don't understand the potential it really has and then get confused. Keep referring all the fediverse sites as the fediverse and it can bring people to the smaller instances and not think that if they're not on Lemmy or Kbin that they have to make some kind of choice on which "site" to join.