Yes, we used "Sicilian" and "French". But there are no official names.
Names for Openings

Mainline sicilian-kan (gremu's bishop out)
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m9-l9
2. Qg1-j4 .. b8-c8 .. Bi14-g12 .. m8-k8
Sicilian-kan classical
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. g13-g12 .. m9-l9
Classical
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8
2. Qg1-j4 .. Qa7-b7 .. Qh14-e11 .. Qn8-m8
Scandanavian / (e4/ "Skywalker" attack)
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. h13-h12 .. m8-l8
2. Qg1-k5

Ah, ok.
So I have been calling this the 'Zebra' opening...
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8
Which of course I could say has the 'classical' variant

So, if any good players would like to help me out, I have a question about one of the openings. I have never seen this played, and I would like to know why. I assume it has some fatal flaw...
Sicilian-Kan Accepted
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m9-l9
2. Bi1xd6 ..

So, if any good players would like to help me out, I have a question about one of the openings. I have never seen this played, and I would like to know why. I assume it has some fatal flaw...
Sicilian-Kan Accepted
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m9-l9
2. Bi1xd6 ..
So in teams, pieces, and especially pawns, are secondary to tactics and position. This is the following move, both attacking the bishop and opening the queen, which is brought out early in 4 player chess.
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m9-l9
2. Bi1xd6 .. Qa7-d4

Alekhine Defense
[Variant "Teams"]
1. h2-h3 .. Na10-c9
Sicilian-English
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. i13-i11
Sicilian Saragossa
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. i13-i12 .. m8-l8

Mainline Valger variation or Sicilian-Nimzowitsch variation
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. Nn10-l9

So... no so much fatal as just not advancing as much as you'd like?
If you have ever seen any attacking games by Tal, Fischer, or a crazy computer, it's kind of like that. Pieces hanging left and right, sacrificing everything for the checkmate finish.

Here is a good example:
http://www.chessgames.com/perl/chessgame?gid=1139475

Wow, this is great guys! I've posted what I have so far, a bit cleaned up and organized, below. Keep it coming.
One question: So far every single opening begins with h2-h3... is that the way it is? Is the 'Black' Opening (my name) so powerful that there is really no other good options for red??
Opening List so Far
Opening Black
[Variant "Teams"]
1. h2-h3 ..
Sicilian Root
[Variant "Teams"]
1. h2-h3 .. b6-d6
Sicilian-kan classical
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. g13-g12 .. m9-l9
Sicilian Mainline
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12
Mainline sicilian-kan (gremu's bishop out)
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m9-l9 2. Qg1-j4 .. b8-c8 .. Bi14-g12 .. m8-k8
Mainline Valger variation or Sicilian-Nimzowitsch variation
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. Nn10-l9
Sicilian-English
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. i13-i11
Sicilian Saragossa
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. i13-i12 .. m8-l8
Zebra Opening
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8
Skywalker Attack
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8 2. Qg1-k5
Classical
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8 2. Qg1-j4 .. Qa7-b7 .. Qh14-e11 .. Qn8-m8
Alekhine Defense
[Variant "Teams"]
1. h2-h3 .. Na10-c9

> One question: So far every single opening begins with h2-h3... is that the way it is?
There are many games with g3 and also with f4.
You can add annotations and create variations:
So, you can combine all the openings and make 2 PGN4 files: FFA and Teams.

> One question: So far every single opening begins with h2-h3... is that the way it is?
There are many games with g3 and also with f4.
Great. I've added that. I haven't found many myself... is there a way to search the archives for openings?

A yesterday's 1.f2-f4 game: https://www.chess.com/4-player-chess?g=150550-1
P.S.
No way to search for openings now.

Skywalker Attack
[Variant "Teams"]
1. h2-h3 .. b7-c7 .. g13-g12 .. m8-l8 2. Qg1-k5
My work here is done
Has anyone named any openings for 4pc teams yet? I was thinking of writing up something, but didn't want to make up my own names if something was already available. (You know, like English opening, or Sicilian, etc.)