A TFF-themed Linkshell (or guild or whatever they decide to call it)

[Andromeda]

A linkshell is a group of people that have an item that allow them to talk together across the game world regardless of location. Depending on what they plan to do it can be a group of people wanting to gather for doing end games stuff like beating monsters that require a lot of people and teamwork from people you're familiar with. In our case we'll be mostly using it for socializing and helping each other out since you'll be able to quickly talk to someone and call them for help.

[Zargabaath]

Hmmm... ... ... how about "The Fuzz" or... ... "Eorzea TFF Legion".

I'm not feeling a level of epicness though with TFF placed somewhere in the name, unless it was put in the cleverly. Let me think some more... ... ... ...

How about the "Guild of Calamitous Intent", a page from the Venture Bros.

The "Inglourious Basterds" to pay homage to Tarantino.

We could try to take some organizations from the Final Fantasy series itself:

The Red Wings (though that may be misconstrued with the hockey team)
The Dawn Warriors
The Returners
Avalanche
SeeD
Tantalus
Zanarkand Abes
Ivalice... the world nobody wants to live in do to constant warfare on a gargantuan scale. (long? yes. true? yes.)

"Cid"

"Sakaguchi's Army"

"U.S.A." Did I get anybody with that? Thinking I was talking about the United States. What it really is: Uematsu. Sakaguchi. Amano.

"The Void" we are everything and nothing.