黒渦団 -The malesrom
黒 is black 渦 is vortex or malesrom, 団 is group.Kinda thought it was wierd lookin name.

不滅隊 - Immortal Flames
Immortal Flames in Japanese is 不死隊 or 不滅隊.It comes from the Immortal (Persian Empire)

双蛇党 - The Order of the Twin Adder
双 means twin 蛇 is snake witich is Adder, 党 is group.

Kanji is complacated, it makes it wierd to just translate it in English to Japanese or Japanese to English. The Black Shroud is 黒衣森. I can tell its just translated:-/