Can't assume google/facebook/twitter were successful because of a master plan that hinged on their name; their success doesn't strongly imply they were named well. Anecdotally, facebook was originally "The Facebook", google was originally "Googol", Twitter was once "twttr", and Apple was named on a whim when nothing could be decided on.
Bayesian is an alien word, I still remember wondering what it was when I first saw it. Repeating a word/name aloud is the recommended way to remember them on first impression, and memorability matters, but encouraging that kind of memorability is a small factor anyway, just for the record.
Edit: Whether or not my ideas are good, I disagree that the importance of immediate reaction is overrated. It's hard to say precisely how it has been "rated" in the conversation, but I think it matters a lot in framing the ensuing seconds of conversation.
"Applied Insight" [...] has the same initials as "Artificial Intelligence" which I'm not sure if it's a minus or a plus.
Can you imagine anyone's opinion being altered by such a thing? Its value rounds to zero (It's nonzero, but the smallest credit the human mind could give it is, I suspect, too much).
Forget cleverness for its own sake, optimize for the consequences.
someone reads "InSight", their brain says "oh, I get it, they combined insight and in sight. Their name is a pun." imagines suited marketing man. Where do you want to go for lunch?
Capturing that first thought and directing it somewhere useful is crucial
One obvious question: when is the name most important? When first heard; Introductions.
Some common names take the form of "[identifier] [word for a group]" or similar, eg: [Rationality] [Institute]
Use online thesauruses to find synonyms for good words, make long lists of words to combine. http://thesaurus.com
Google how to come up with good names, skim chapters in marketing textbooks for meta-ideas.
Don't react fast/naturally (eg: "the name Waterline is a clever meaningful in-group signal and sounds pretty."), ask yourself how your target will react (eg: "what's that, whale environmentalists?").
Who are your targets? Intelligent ambitious young men or their uninterested 45 year old mothers? Academics? From which field? etc.
Common reaction to mention of the group will be to assume their arrogance (suggesting they can teach smartness, that they have smartness), behaving guarded but curious.
Suggestions: Insight House/ Bayesian House
Reaction: "what does bayesian mean?" it's the math (credibility+++) of how to decide (arrogance-) etc. Bring evidence into discussion if target identifies as being "logical" (young smart men).
PM me if you want my opinion without revealing the name in public.