Dang I totally forgot all about that term. Been awhile. Well it eventually reduced to "surfing the net".
The thing about the internet, is it was the thing to make it only one net. Previously there were weird systems like bitnet, VMSnet, where you had to juggle email address encoding standards to get balkanized college campus networks to talk back and forth to each other.
"The web" became the subset of the net, that worked with web browsers. Only one thing.
Was there a "The Facebook" period? Or was that just a movie name?
So then we passed through a period of brands. Reddit is a brand. It is not altogether surprising that people would refer to the fediverse in terms of brands. Lemmy, kbin, beehaw, whatever.
Email and the web had/have specific protocols associated with them. The fediverse has multiple protocols. We're using ActivityPub, which seems to have won as a standard. It isn't exactly catchy or smooth flowing off the tongue.
Ok, if we try to brain crunch all these previous trends, here's what it's going to be called, if it hasn't been already:
THE VERSE
The difference between the fediverse and the universe will be forgotten. Linguistically, people will not keep up with that detail. Only old timers / early adopters will notice that linguistic change.
Possibly, 'verse' will come to be seen as short for multiverse.