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!".

We will need better robes.

That is my favorite name so far.

It is an advantage for a name to include a word that has "juicy" connotations, in contrast with words like rationality, institute, decision, making, water, line, study, practical, critical, insight.