This is why you should never geeks - including me - decide branding issues.  :-)

"Exposed" is a case in point; it's a negative concept.  People die of exposure. You might be naked and exposed. The word "expose" generally is associated with connotations where "exposure" is a bad thing.  

Sorry Aaron, but the very example you cite is about "indicating a lack of protection".  

That's not how I feel about the Onion sites I run, at all; in fact the onion "technology" (call it that for the moment) adds value to what is otherwise a normal, safe, secure "public" site.  

I've written elsewhere that if people use a site over Tor then they probably have a good reason to do so.  The reason for running a public onion site is so that those people have a better experience and enjoy the benefits of end-to-end authentication. 

They are experiencing a positive benefit from onion services, rather than a negative one; thus they should be using a kind of site with a positive name, rather than a negative one.

All qualitative labels will have this problem: Free, Libre, Open, Closed, Hidden, Public, Private ... all of these describe an abstract intent, rather than a technology.  Such qualitative label-names are inevitably presumptuous of {some} implementer's intent.

One can at least support "NonHidden" because it is the inverse of Hidden, but if "Hidden" is to be deprecated (?) then that seems silly. "Overt" is a variation of the same, the word literally means "not hidden".

David says that this is "going to be part of the ABI" - in which case I am amazed that we're having this discussion because config file contents are free to be disjoint from branding, and can be as insane as you like.