Does anyone know what this opener is called?

After move 3 you have the standard position in the Two Knights Defence, reached by a slightly unusual move order (W usually plays Nf3 before Bc4). 4. Ng5 is also standard (there are quieter alternatives like 4.d3) and 4...h6 is a gross blunder. More usual for B is 4....d5 or 4...Bc5.
1. e4 e5 2. Bc4 is the Bishop's Opening. It's rarely played but it's perfectly viable.
2. ...Nc6 A slightly unusual choice, but at a glance I don't see anything wrong with it.
3. Nf3 transposes the opening into the Italian Game, which is more commonly reached by 1. e4 e5 2. Nf3 Nc6 3. Bc4 (i.e. the bishop and knight are moved in the opposite order).
3. ...Nf6 is the Two Knights Defence, which is a common way for the Italian Game to proceed and a very solid opening for both sides.
4. Ng5 is a very common line in the Two Knights Defence. White is almost certain to win a pawn but Black has good counterplay to compensate.
4. ...h6? At this point this isn't a recognized opening any more because it's a bad mistake, losing the exchange immediately.
Did that answer your question? But anyway, this opening isn't weak, up until 4. ...h6? it's a pretty standard opening. I dunno why you think it only works against basic players.
EDIT: Dammit, I was ninja'd twice. Sheesh.

Well, Dr. Tarrasch thought that 4. Ng5 was a patzer's move.
But, we're living in the 21st century now...

Well, Dr. Tarrasch thought that 4. Ng5 was a patzer's move.
Not if it works out tactically though.
I remember a long time ago where I played 4...h6??, my idea was that after Bxf7+ K moves the knight is under attack, so the bishop or knight should be lost, but somehow I didn't consider Nxf7. I mean ...h6 is basically asking the knight to do what it came to g5 to do!
The correct move of course is 4...d5 5 exd5 and I believe ...Na5 is supposed to be best, instead of opening the center immediately the knight wins a tempo on the bishop and hopes to get compensation for the pawn because of white's now awkward pieces (since white played the aggressive Ng5).

Well, Dr. Tarrasch thought that 4. Ng5 was a patzer's move.
Not if it works out tactically though.
I remember a long time ago where I played 4...h6??, my idea was that after Bxf7+ K moves the knight is under attack, so the bishop or knight should be lost, but somehow I didn't consider Nxf7. I mean ...h6 is basically asking the knight to do what it came to g5 to do!
The correct move of course is 4...d5 5 exd5 and I believe ...Na5 is supposed to be best, instead of opening the center immediately the knight wins a tempo on the bishop and hopes to get compensation for the pawn because of white's now awkward pieces (since white played the aggressive Ng5).
Yup. This is the Oops-Black-Blundered-into-a-Knight-Fork variation of the Two Knights Defense.

fried liver
This is the Fried Liver Attack. I'm amazed that so many people didn't recognize it...
http://en.wikipedia.org/wiki/Fried_Liver

No, it would be the Fried Liver if black could take the knight on f7. If he just loses his h8 rook to the knight, it's called black blundering.
fried liver
This is the Fried Liver Attack. I'm amazed that so many people didn't recognize it...
You really should look at the pages you link to more carefully, the Fried Liver occurs after the pawn exchange 4. ...d5 5.exd5 Nxd5; the key point being that the knight is now undefended so it's a sacrifice.

fried liver
This is the Fried Liver Attack. I'm amazed that so many people didn't recognize it...
Fried Liver comes out of 4...d5 then 5. exd5 Nxd5 then the naming move it the Knight-sac of 6. Nxf7.

fried liver
This is the Fried Liver Attack. I'm amazed that so many people didn't recognize it...
You really should look at the pages you link to more carefully, the Fried Liver occurs after the pawn exchange 4. ...d5 5.exd5 Nxd5; the key point being that the knight is now undefended so it's a sacrifice.
Thank you.
Oh, sorry. I should have stated before that the h6 was just a pointless move to show what the intention of the white opener was. Anybody who looks at the board and tries to think what their opponent is doing can stop this with very little effort which was why I said it was probably only useful against novices.
Oh, sorry. I should have stated before that the h6 was just a pointless move to show what the intention of the white opener was. Anybody who looks at the board and tries to think what their opponent is doing can stop this with very little effort which was why I said it was probably only useful against novices.
That's not exactly true. While only a novice would walk into Nxf7 (caveat: I only mean Nxf7 as a rook-queen fork without counterplay for Black - it's fine for Black to allow this move as a sacrifice in the Fried Liver Attack, or if you want a really tactical game then the Wilkes-Barre variation allows this rook-queen fork in exchange for strong counterplay); this opening is perfectly solid for both sides if Black plays d5 to block the bishop and gain counterplay by gambitting the pawn.