I noticed that I almost upvoted your post because it was an in-group thing to say and not because of its actual merit in this conversation. Having the word 'conspiracy' anywhere near the name of this organization would be a downright awful idea in practice. I'd as soon suggest changing the official LessWrong slogan to "We're Not A Cult!".
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.