Bogo-Indian opening//
double fianchetto

It limits the movements of knights, making any opening involving knights that much more complicated.
I wouldn't recommend it, but it's theoretically sound.

It's not called bogo-indian (the bogo-indian is a black defence against 1.d4; 1.d4 Nf6 2.c4 e6 3.Nf3 Bb4+ is the starting position)
You can go for an immediate double fianchetto with either white or black, but is not a great idea in both cases; the whole thing is not very flexible. Expecially as black defending is not easy; a premature 0-0 can lead to a deadly assault on your king and in general white position is much easier to play. I encounered the variation only once in correspondence play; in the resulting game black failed to create counterplay and as a result went down without a fight. He could have obtained a fairly equal position after the opening, so the game is not theoretically significant, but i think it shown how the positions are usually much easier to handle for the white players.

I don't know if it has a name; it's more a system than an opening and can arise by trasposition from both the modern and the english defence. I think this is usually just called "double fianchetto".

It is mainly played to pin the rook if the bishop on the other side moves andif the knight doesn't move.
Usually if this is the case then the bishop will choose to go to g7 or b7

bresando's given you some good advice and I would pay attention to this post.
The double fianchetto system with knights on f6/c6 is extremely limiting as the bishops are blocked by the knights - it's much stronger if they are placed on d7/e7. With that setup, it is difficult for white to just blindly break through as he often crashes against the wall black has setup. However, black's setup is rather passive and non-coordinated for attack. There are ways for white to have a comfortable game though...
The double fianchetto is also referred to as The Hippo. It can be quite powerful in the hands of a strong player, but many play this as they believe it requires no theory and can be played blindly.
Personally, I believe it's much stronger to fianchetto only one bishop and use the other to harass your opponent. Fianchetto's can be blunted by pawns chains or have their pawn structure picked apart.
A good friend of mine likes to fianchetto both of his bishops right away.Is there a name for this opening?