The Black Organization is called the Black Organization by low ranking members of the Organization that don't know anything about the syndicate, only that they wear black like crows which is why they call it that. The true name is suspected to be known only by high ranking members and the boss.
Gosho has said the name of the boss will be revealed after the true name of the organization is revealed... which means the Black Organization is not its true name. Supposedly, the name of the organization (the real one we don't know yet) has something to do with the boss's name in it. But that will probably be revealed at the end of the series, which won't be for a long while.