Please note that I'm talking about the moves that WHITE is playing here.
What is this opening?

Please note that I'm talking about the moves that WHITE is playing here.
No opening is based on White moves. All openings are based on both colors.
For example:
1.e4 e5 2.Nf3 Nc6 3.Bb5 is the Ruy Lopez
1.e4 c5 2.Nf3 Nc6 3.Bb5 is the Rossolimo
Yet White's moves are exactly the same.
Another:
1.d4 d5 2.Nf3 Nf6 3.Bf4 e6 is the London System
1.d4 f5 2.Nf3 Nf6 3.Bf4 e6 is the Dutch Defense, often dubbed the Dangerfield Attack
Yet another
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 with a subsequent f3 and Qd2 is the English Attack
1 e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 with a subsequent f3 and Qd2 is the Yugoslav Attack
So again, there is no opening solely based on White's moves. All openings are based on both colors. Both sides are playing the same opening. Many mistakingly say that after 1.d4 Nf6 2.c4 that White is playing a Queen's Gambit. He is not. There is nothing he is gambiting. If the game proceeds 2...g6 3.Nc3 Bg7 4.e4 d6, it is a Kings Indian Defense. Both players are playing a game where the Opening is the Kings Indian Defense. One player is playing the White side of it and the other is playing the Black side of it. But all games are a SINGLE OPENING based on the moves of BOTH players!

This position looks as if you (White) were going for a Giuoco Piano (aka "Italian Game") position but Black decided to play an irregular version of the Hungarian Defence.

The Guioco Piano can go...
which is a bit similar.
But if Black plays differently (The Hungarian Defence which is characterised by ..., Be7) we could have:
...and that starts to look rather like the position you gave us. These are not the best moves: they are only intended to explain why I think what I said about the possible opening names.
So.... uhhhhh. I commonly play this opening of WHITE at my elo rating currently (900-1000) but I've seen no one talk about this, and other people play it against me too. I just consider the moves to be standard development or something. Did I invent a new system, or is this just an unpopular one that no one talks about?