Somebody more knowledgeable than I will probably provide a better answer, but if you were playing white, you used the English Opening. If there is a specific name for the variation played, I don't know what it is.

Well, whatever color you were, it is called the English Opening.  The English Opening normally revolves around a clamp on the d5 square.  If you can see, c4 - Nc3 - e4 all clamp down on d5.  There is a lot of wonderful things to learn in this opening... Go online and order a book starting out - the english opening.  f3 isn't bad - after he retreats the bishop you can play d4 and you are pretty much into a king's indian, except he hasn't got the bishop to g7 - you have a definite plus in space. 

 Anyway, 1. c4 is the English.

imo it has transposed into a pirc defence - the game won't proceed on English lines anymore.

 

This reminds me of a Maroczy setup, but that weak d4 pawn will be awful unless you can make that break.  Bg4 was a crap move and you get a huge center.  Then it might even transpose into the King's Indian Saemich with a tempo down for Black 

thanks.

1. d6 is completely unnessecary, and the most likely situation where this would arise is a pirc player trying to apply the pirc to everything.

2. e4 is inaccurate in this instance, as its just making it into a target, and not taking advantage of blacks mistakes, although its not actually going to hurt white.  However, its only inaccurate as e4 is likely to be played regardless, but it certainly should have been held in reserve.

3. Bg4 is a mistake as well, as f3 immediately is worse for black, or Nf3 with careful play can be convert it into a loss of tempo and thus worse for black.

As of 3.Nc3, this is still just the English, but with transpositional possibilities to the King's Indian, Old Indian, etc. 3...Bg4 is a bad opening move that wastes a tempo. So after 3...Bg4, we are no longer in any typical opening variation, and the game would just be classified as an English.

 

It could not transpose into a variation of the KID Saemisch unless white decided to also waste a move. It could end up looking like the Saemisch, but it will have completely different themes with the missing black tempo.

 

People pointed out the transpositional possibility to the Pirc, but this is false as c4 has been played. One of the characteristics of the Pirc is the Queen's knight being placed in front of the c-pawn.

 

Killabeez pointed out the problem of the undeveloped d-pawn. Some experts might disagree with us and say that white's strategy of a delayed d2-d4 break is just fine, but I personally agree with Killabeez that this is a problem with the move order you played. If black had used his third move to play 3...c5 or 3...e5, he would have had a much easier theoretical shot at equalizing. I think you should have played d4 before e4. Then again, I also think you should have played d4 or e4 before c4...

 

~TO 

I looked at it and the first thing that came to my mind was that d-pawn must develop on the very next move as it serves a dual purpose in establishing a stronger hold on the center and unleashing the dark square bishop. Black is not playing aggressively enough in the center and is wasting time with the bishop which can be easily driven away by the king side pawns. Blacks pawn on d6 also severely limits the scope of his dark square bishop. You should be teaching him the error of his ways from this point forward. 

 

It is the English Open Crap Variation ended at move 4.

 

1. e4 creates holes in your camp. The kingside minor pieces will now have difficulty developing normally as the Knight and Bishop get in each other's way. A bishop on d3 is simply weak. If you move f4, trying to free the knight...er...you lose the queen depending on where the bishop is and a tempo otherwise.

1. c4 d6 is already a mistake by black, 2. f4 would have been interesting as black as no immediate threats, you have not yet decided where your central pawn structure.

2. d4 Nf6 becomes kinda an english defense in response to 1. d4.

3. Nc3 e5!? I've had this played against me before.

"1. e4 creates holes in your camp. The kingside minor pieces will now have difficulty developing normally as the Knight and Bishop get in each other's way. A bishop on d3 is simply weak. If you move f4, trying to free the knight...er...you lose the queen depending on where the bishop is and a tempo otherwise."

 

It's funny how people see things differently. You see white's opening as bad but I see it as establishing an early hold on the center and a space advantage. Blacks position is already cramped and any challenges to the center are easily met. In forcing the bishop away, white also establishes the beginnings of a stone wall with the king side pawns, weakening blacks bishop.I also don't see how Bd3 or Ne2 or particularly weak as both add pressure to the center, although there are better squares for them to be developed to. So we come out of the opening and black is cramped, has no control over the center and both bishops are rendered ineffective. I could play this against a lot of players here and come out ok.