To men of honour belonging to the organization, there is no need to name it. Mafiosi introduce known members to other known members as belonging to "cosa nostra" (our thing) or la stessa cosa (the same thing), meaning "he is the same thing, a mafioso, as you". Only the outside world needs a name to describe it.
+w+ i see hibari ~ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥
i think you should do byakuran, jin-san... i bet it'll look good on you~