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.
That really sounds like an unnecessary constraint. It's not as if the only thing people are going to hear about the organisation is the name; presumably they'd also hear something about what it does.
In my view, a name that doesn't need to come with an explanation is worth more than a name that makes for good in joke.