Saying "Fediverse" is too broad, like talking about "the Internet" when one is talking about Reddit.
Saying "lemmy" -- currently the most-widely-used software package to do a Threadiverse instance -- is too narrow, and excludes kbin and some other software packages.
"Reddit-alike" doesn't seem ideal, as I'd imagine that the Threadiverse will evolve past whatever Reddit has been and already differs in some ways. I'm also not really enthralled in terms of branding the thing in terms of Reddit.
I don't intrinsically feel that "Threadiverse" has to be the term for that, but I do think that there's a need for a term for that. It's the only term I've seen used so far for it.
It does rely on punning on "Fediverse" and sounds similar, which I regret a bit -- I think that it might be nicer if it sounded more different, so that one couldn't perhaps mistake one term for the other. But I'm generally okay with it, myself.