It doesn't seem to stand for anything, none of the major key names are acronyms or have any meaning. Turks is just simply what they are called, same with SOLDIER, and same with AVALANCHE. Course its not like FF was known for actually explaining where their terminology comes from but unless someone like ShinGundam or The Crystal remembers the Ultimania's mentioning where they got the names, it's pretty safe to say its just there to sound cool.

Turk itself is just a short hand term for the ethnic people who live in Turkey. So your guess is as good as mine.