Death Note; Apple Alliance (very obscure), some single letter name (if allowed), IPO, something with shinigami in (but then you'll most likely be associated with Bleach), REM (also obscure).
Gundam Seed; come on, just call it ZAFT, PLANT, ORB or the Bloody Valentine Alliance.
WHR; Hmmm, haven't watched enough of this to give you a nice name...
Naruto; So many organisations I'll just wiki them. Earth, Wind, Fire, Mist, Water... Alliance, I personally like the Six Paths of ZAFT or something along those lines.
So heres my recommendation: The Six Paths of ZAFT/ORB.