I get you. In the end, for me, and I settled on this a while ago, "Fediverse" is a bad name. It's confusing, seems like a Marvel thing, sounds weird and even unappealing frankly. Mastodon works because it's a cool appealing word. It's not just twitter refugees and their ignorance. The "fediverse" has a marketing/branding problem. And if you want "refugees" or "migrants" (which I acknowledge are problematic terms for actual IRL refugees, sorry), you've got meet them where they are.

Additionally, platforms are actually products. In fact, relatively vertical products with often sub-par interoperability for something that claims to be the "next internet protocol". So, whether you create some branding or not, "you", as a platform, are putting branding out there even if it's the absence of an attempt.

So my recommended approach would be to happily "brand" a platform, but always be pushing and clarifying that it's on the fediverse and what that actually means. Also, I'd start talking about "the social web" rather than just the fediverse, because that's what it is and it's a better term IMO.