The "Fight Club" allusion is good, though. Instant recognition if you can manage to activate that node, and it ties in well with the idea of a rationality dojo.
Combining that with other ideas you'd get "Insight Club".
"Rationality Dojo" hasn't been suggested.
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.