That formation does not have an official name. You would need to specify the move order for both sides before it could be classified.
I call what you are doing the "queenside bubble". If you did a sequence like that on the kingside it might be called Leningrad Dutch.
I have looked into the Leningrad Dutch in reaction to your comments and it appears to be an aggressive defense for 1. d4
I liked what I saw in the games I reviewed and was inspired in a couple ways.
However, I did not find anywhere that a white player would employ such a layout. I am curious what defenses one should employ vs this formation in white, and what tricks white can use with it.
In high school one player suggested that the strongest defense of it as an opening is to mirror it.
Also, I noticed that pushing the rook pawn was often unnecessary due to the tendency of white to develop in ways that did not attack the g6 (whoops not f6) square.
I'm not sure about the safety of the pawn formation around the King, particularly as White on the Kingside.
In a little used variation of the King's Gambit, Black deliberately forces white to do this very thing:
This is why I never push either of the center pawns for two to open up. The center pawns lay behind for possible defense of the formation.
Also, 4. d3 in that King's Gambit scenario would not be a terrible maneveur imo. It is part of the basics of what I would do kingside and allows the bishops to develop if 4. ... xf4
...if not white has 4 developped pawns vs one developped pawn and a queen that i would call out of position.
I have looked in the Bird Opening. It appears it is a kingside version of this but it involves pushing the king's pawn instead of the queen's pawn. It locks the dark bishop in unless it follows a pice exchange or wanders off to the left side of the board. I like mixing it up in the center with my bishops, or at least having them support the action there.
My preference for defending the f pawn in the white kingside version is to use my dark bishop to support (by d3 at some point), or push the g-pawn one space to form a pawn chain.
I may experiment with this Bird opening anyway, it is very different than what I do and might give me some cool ideas.
I open as white with a formation that I use on either king's side or queen's side as per whim. As black I often incorporate such a formation as part of my defense.
However, I cannot identify the opening and am interested in refining my use of it.
The basics are:
1) pick a king or queen side.
2) push bishop pawn 2
3) push knight pawn 1
4) bishop gets underneath knight's pawn
5) knight get's underneath bishop's pawn
6) Off side royalty pawn (queen if king's side, king if queen's side) pushes one.
7) (king side castling is available) pushing the side pawn by 2 often engages the center of the board properly (king if kingside, queen if queenside)
(8) Often I push the side's rook pawn one to counter knight development.
Please help me identify this opening and give me pointers on it.