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.

The name of "organization" is vague and general.

But... maybe this name is used for keeping consistence with Chinese version? Now that Chinese name isn't so mysterious, the English name should also be plain too.