The lemmyverse sounds perfect, but it ignores alternatives like kbin etc. It would be better if we didn't end up with the situation we have with Mastodon where people assume Mastodon is the fediverse.
So, what do we call this little niche in the fediverse?
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.