Lemmy is a technology where each instance follows the same rules: acompatible federation API. You want people to know your website is a Lemmy instance.
I kind of see where you’re coming from, and I think the reason I wasn’t thinking of it in those terms is that I see ActivityPub as the more important underlying tech across the fediverse than say Lemmy/Mastodon/Friendica/etc.
I say that in part as I’ve come into the fediverse from Mastodon, where there’s more than two options in play, e.g. Akkoma/Firefish/Misskey/Pleroma/etc. each of which has some commonalities, but also some pretty distinctive features, particularly from the Misskey side. Hell, Mastodon itself even has Glitchsoc, which is what the original instance I joined on that side of things runs.
On reflection, I don’t know that the microblogging instances mix in the name of the software they’re using as much, which you’d think with more options they might be inclined to, but the more I think of it the more I remember a lot of them use some fun, odd names instead.