I encounter this type of position occasionally. In the diagram, black is to move. (The position can also occur for white.) The opponent has castled but lacks a king knight for defence. It is tempting to attack with the queen, knight and two bishops.

Does this position have a name?

The obvious way to attack starts with Bxh2+:

But of course the opponent's moves are not all forced here. The king can move to g3 after the knight check, and it doesn't even have to take the bishop at the start, but the complications are too much for me.

Is this a well-known winning position or a well-known fool's errand?

Either way, does the position have a name?

It's called "Greek Gift", correct, and it fails in this position. If your Pawn were already at h5, it might work.

Whoa thanks guys, exactly what i needed.

https://www.chess.com/article/view/the-greek-gift-sacrifice-lives-on

I found that quite interesting. There was also a massive article in 3 parts (was it by Silman?) somewhere on this site that goes through everything to do with the Greek Gift. Maybe someone else knows where that is and can link to it? I can't seem to find it atm. 

Here it is. It was under Classical Bishop Sacrifice. 

https://www.chess.com/article/view/the-classic-bishop-sacrifice-part-one

https://www.chess.com/article/view/the-classic-bishop-sacrifice-part-2

https://www.chess.com/article/view/the-classic-bishop-sacrifice-part-three

Wow thefinalDave thanks for that! Even more exactly what I needed. Here's the game I recently played which prompted this thread. My opponent declined to take the bishop and this happened ..

But I see now what I need to be prepared for next time ..

Vukovic's Art of Attack also discussed the Greek Gift at great length

Looked up Vukovic and also found this recent book published in 2011:

Sacking the Citadel: The History, Theory and Practice of the Classic Bishop Sacrifice

Four hundred years ago, an Italian chess master, Gioachino Greco, discovered an extraordinary bishop sacrifice on h7 that often leads to checkmate or a significant material advantage. More amazing still, he recorded the idea! This book chronicles the history of that idea, what many have come to call the Classic Bishop sacrifice, from its discovery and formative years through its remarkably complex uses in modern chess. During the past century, several annotators have attempted to explain the circumstances under which the sacrifice works, and when it doesnt. Edwards reviews their efforts and, in a spectacular ninth chapter, provides a modern classification. His taxonomy of the sacrifice is comprehensive and full of pleasant surprises for beginners and even accomplished masters. This book represents a thematic approach to chess tactics and strategy. Careful readers will suddenly discover that they are able, quickly and accurately, to see 5-10 moves or more ahead in these lines. Here you will find hundreds of carefully annotated games. Learn from brilliant moves and strategies; and take full advantage of others instructive mistakes.

https://www.amazon.com/Sacking-Citadel-History-Practice-Sacrifice/dp/1888690747

Also featured on Silman's website:

http://dev.jeremysilman.com/shop/pc/Sacking-The-Citadel-p3641.htm

A whole book on this position is more than I could ask for. The cover pic is a bit dramatic though.