Can someone please tell me what opening this is and what should my next move be? Thanks!

A quick search indicates this is called the Balogh Defense (or a line of the Dutch Defense Staunton Gambit). If this is a game in progress, you're not supposed to ask advice, but you can use the different resources available to help navigate the opening.

Thanks! The game is in progress but we're well beyond the opening. I responded with Nf3 but I don't think that was the best move.

exf5, I'm sure you shouldn't even consider letting Black get away with that. Maybe something like this?

The Baloghna?

Thanks rooperi. The only issue I see with that could be black's 2. g6 but perhaps it will cost him later.

Hmm. I'm thinking maybe Nc3.

Janos Balough was a Hungarian/Romanian Master of the 20th century (1892-1980).  He was good enough to play in a few Olympiads and was once the Romanian Champion as well as an IM of correspondence Chess, but is best known for the oddball opening named after him.  It's one of those openings that there is not much book on it simply because it's a dubious idea, although maybe good for surprise value.

Don't trust computer recommendations in the early opening (unless of course it's part of their book).

Why? 

I was already suspect of Nf3.. Once Naum made that move it actually froze and lost on time. 

Computers are terrible at openings (and the earlier it is in the game, the worse they are).

Interesting, I wasn't aware of that. Thanks tonydal. 

To me it looks like a kind of Staunton Gambit against the dutch defense.

see:

http://en.wikipedia.org/wiki/Staunton_Gambit