This variation is uncommon, but it's certainly not unheard of. I don't know of a particular name for it, and rather than get bogged down in the endlessly-analyzed lines, let's just take a quick, objective look at what this move accomplishes, and what it gives up.
Advantages
3.Bc4
aims, as you said, at the f7
pawn. If allowed to remain on the diagonal, this Bishop could provide pressure against the Black kingside in the midgame.
- It develops the Bishop quickly, allowing White to castle kingside immediately if he so chooses.
- It may avoid trading away the Bishop for Black's QN or QB like we see in the Canal-Sokolsky Attack (
3.Bb5+
) or other variations where White's KB lands on b5
.
- It grants White some additional influence over the light central squares weakened by Black's first two moves (
c5
and e6
).
Drawbacks
- By developing to
c4
so early, this move appears to invite Black to play ...e6
, immediately limiting the Bishop's scope and possibly requiring a future relocation.
- On
c4
, the Bishop is vulnerable to space-gaining queenside maneuvers via ...a6
and ...b5
, or ...Nc6-a5
.
- This move does not provide any immediate threats, so Black is free to continue to choose a system as he pleases.
Ideas
Looking at these two lists, a picture begins to form of the themes for both sides.
White will likely try to hold onto this Bishop, to assist in his kingside operations. He will likely play 4.d3
to keep the position closed, and to cement his hold on the light central squares.
Meanwhile, Black may use the Bishop's placement as a convenient way to make his thematic land grabs on the queenside. Black is not compelled to respond in any particular way, though my database suggests that a Dragon-like setup with ...Nf6, ...Nc6, ...g6, ...Bg7
is slightly more popular in this line than the ...e6
variants.
[FEN "r1bq1rk1/pp2ppbp/2np1np1/2p5/4P3/1BPP1N2/PP3PPP/RNBQ1RK1 w - -"]
1. e4 c5 2. Nf3 d6 3. Bc4 Nf6 4. d3 Nc6 5. c3 g6 6. O-O Bg7 7. Bb3 O-O
Conclusion
This third move choice from White, while unusual, does not seem to be downright inferior. It suggests a tense, positional midgame, with each side operating on his better flank. Good luck!