I won't go into details here because we have a first time watcher, but while they never used the name again, you can clearly tell when that particular group is up to shenanigans later on down the line. Pretty much anything shady involving Earth, telepaths and advanced tech (human or otherwise) is most likely them.
Personally I think that it works better if this shady cabal doesn't have a particular name, because that's not how massive conspiracies work. Not advertising the fact you exist is kind of the whole point, and I always roll my eyes in fiction whenever there's a secret organization with an actual logo and other trappings. Real military-industrial-mega-corp type conspiracies don't operate like Bond villains with volcano lairs, uniformed henchmen and tanks full of laser sharks. They're an assemblage of informal agreements held together by common goals and enforced by mutually assured destruction leverage, and they're in constant flux since it's hard to keep such things going over more than a generation.
With that in mind I prefer to think of Bureau 13 not as a real entity, but one of many many code names for a line item on the black budget that allows them to syphon funds for whatever they may be up to. All that said, IIRC the Psi Corps books make mention of a Department Sigma, which is either the same group by a different name, or just the faction within that group that operates inside the Corps.
I try to keep my responses short and vague, and only about an episode reviewed by a first time watcher, for the same reason.
