My concern with the name Stealth Address is that it will end up being a niche feature that most people will not use. Peter's "Ohh, privacy is good!" argument makes sense among his peers, but will fall flat on most common users. Most people "Have nothing to hide" and aren't threatened by privacy, even with all the leaks and damage done. This should be viewed as a standard and non-scary option, and not something for criminals and troublemakers only. Stealth has those connotations, and I have a feeling it will become put in a corner. I think he is also a bit biased in that the super-plugged-in people (aka meetup attendees) have heard of this term and it's too late to change it. I disagree that it's really that well known, even within the Bitcoin community.
Names seem to fall out of describing how something is used or describing what it does. We should also focus describing traditional addresses as well, to see if there might be a way to relabel them.
No, everyone cares about privacy, at least to a certain degree. Or maybe you could find me someone who would love to show me his bank transaction history.
If this were the case, Edward Snowden wouldn't be hiding in Russia, no one would be using Facebook, and Tor would be standard. For the vast majority, privacy is simply not valued by most people when it comes down to actually put in any effort. The Bitcoin community in general is going to have a selection bias towards those who care more than the average person.
Privacy is valued, when people appear to not care about it the threat is usually not tangible, as in your Snowden, FB and Tor case. When your bank/credit card history is out, or you are caught masturbating you will immediately feel how important it really is. Same happens when your friend/wife just saw your bitcoin transaction to a stripper on blockchain.info.
Also the incognito mode seems so important that every browser maker feels the need to put it in.