You are so right. I implemented browserid when it was named "BrowserID" and it really made better sense (the name was pretty self explanatory). "Mozilla persona" sounds like something that only some obscure subcult of firefox users should use.

I would urge mozilla to remove all branding from the popup. It's gonna get really confusing when 3rd party popups get into the game (would they call it Google browserID or "google's version of persona"?). Second, since websites are not getting any private information from mozilla, mozilla is barely relevant. Third, while mozilla's work is commendable, users don't need a link to learn about the protocol and that it's benevolently "built by a nonprofit", instead they trust that the target website knows what it's doing by showing that popup.