The Singularity Institute wants to spin off a separate rationality-related organization. (If it's not obvious what this would do, it would e.g. develop things like the rationality katas as material for local meetups, high schools and colleges, bootcamps and seminars, have an annual conference and sessions in different cities and so on and so on.)
We can't think of a name for this organization.
We can't think of any names that seem good enough to be audience-tested.
We don't have any ideas good enough that we'd want to mention them in this post.
Help.
I like "Insight" too, but probably not "InSight" as part of the name, feels a bit gimmicky, as markette says.
"Insight Institute" has nice alliteration.
"Applied Insight" has good connotations for caring about effectiveness, as opposed to mere philosophizing. It also has the same initials as "Artificial Intelligence" which I'm not sure if it's a minus or a plus.
Then they could use old "SIAI" headed notepaper to refer to the union of SI and AI!