The setup after b3+Bb2 or g3+Bg2 (or on Black's side b6+Bb7, g6+Bg7)
is called a fianchetto https://en.wikipedia.org/wiki/Fianchetto.
Doing this on both Kingside and Queenside is thus called a "double fianchetto";
I don't think there's a more specific name than that.
1.b3 is called Larsen's opening, while 1.g3 is Benko's opening. They are examples of openings that are collectively called modern or hypermodern.
If you have doubts about opening names, I think the easiest thing to do is play them on a chess engine. Usually the engine will then tell you what is the corresponding name of the opening.