I think that's just because the show has a history of vague, implausible names. "Greater Nazi Reich" is easily the worst one. The book had a Vichy-style United States, which makes a lot more sense.Now that I think about it, the show never told us what form of Communism the BCR practiced. Marxist-Leninism? TTL's version of Maoism?
"You do know we're Communists, right?"
Well, what kind of Communists are you? No one describes their ideology in such a casual, non-descriptive manner.