In English version of Rainblood(雨血), 组织 is simply translated as "organization".

While not literally incorrect, the translation of "组织" as 'organization' lacks aesthetic appeal. A more impactful name would be concise and memorable, preferably three or four syllables. 

In series Detective Conan, the dark organization is called "Company", which might be a nice example. Another case is in Harry Potter, Lord Voldemort is called You Know Who.

The best way might be giving it a formal name, which should be properly translated to other languages. If the author tried to keep it mysterious, "The Syndicate" may be a good alternative, which is often used to refer to a secret criminal group with a strong sense of mystery.