The Umbrella Corporation (stolen from Resident Evil). I figured if a group is going to be conquering planets and engaging in interstallar commerce, who is to say it can't be a corporation? YAH Big Business!

LOL

But really what I call my empire would depend on what empire I am playing on the SoA2 mod, when I play Federation, I just call my empire "The Federation"

I always go with "The Council" for any faction, though I very seldom play Vasari.

I do have a variety of naming conventions for cap ships, however.  I usually run out and start using defaults as the game goes on, though.

TEC: I use the prefix CNV, or Council Naval Vessel.
Kol: Hyperion, Galactica (nerd alert)
Akkan: Audacity, Horizon
Marza: Hellfire, Gilgamesh
Dunov: Saratoga, Arapahoe
Sova: usually go with given names

Advent: I follow the game's convention and omit prefixes for Advent ships.
Radiance: Right Hand, Left Hand
Halcyon: Thousand
Progenitor: Hiigara
Revelation: Vengeance
Rapture: Mindstorm

I used to have a more extensive list but it's hiding somewhere in my hard drive... although I hope the other posters won't mind if I borrow some of their ideas!  There's some great stuff on here, folks.

"Nerd alert" - lol.

My TEC ships use CSS prefix - Consortium Space Ship (as in ship that belongs in the Consortium space). As for the ships' names:

Kol Battleships: CSS Normandy, CSS Omaha, CSS Iwo Jima, ... (World War II battles)

Carriers: CSS Ohio, CSS Nebraska, CSS Virginia, ... (U.S. States)

Battlecruiser: CSS Cornwall, CSS Yorkshire, CSS Edinburgh, ... (U.K. place names. I dunno, I just get the image of British Navy destroyers in my head when using this ship)

Siege Battlecruiser: CSS Volgograd, CSS Rostov, CSS Voronezh, ... (Russian Cities)

Colony Ships: CSS Columbus, CSS Magellan, CSS Cook, ... (Explorers)

Advent: Aurora Illuminate

Vasari: Riskara Brigade

TEC: Bing Bang Boom Inc.

The Greys

I've always called my army Groove Armada.

1 Giant Space Cookie for you sir...

In all honesty, I play the Vasari exclusively and right now my name is...Akarnyeous Legion

Rising Sun Armada, for all factions im too lazy to change it every time

If I ever work out how to name my empire, it's going to be Empire of the Sun.

i name mine 'The Sovereign', i just use the one for all the races, call my first cap the Sovereignty (sp?)