I'm really not sure which direction to go with this then. The term in Japanese is "Ura Maruhage". "Ura" could go in one of two directions:
-Reverse, which works cause it's somewhat a reverse from Tsurulina the 4th under Hydrate
-Under, which I'm thinking of using after looking over the term a bit, which refers to the fact that the Empire lives underground.
I don't think the term is brought out too quickly (Hydrate does appear in the first chapter of the arc with the announcement of the tournament but they really don't make mention of their names for a while after that) so we have a bit of time but I do want to figure out which term to use before I start on the arc.
BTW: You were almost right with the comment: it's Be-bebe that works with Hydrate, not Bi-bibi. Bi-bibi is a problem for the arc after this.