I came across a Japanese person using "Lehman shock" when writing English, and I'd like to know what the most common American English term is. Do Americans use the term "Global Financial Crisis"? Or do they more commonly use the term Great Recession?
Great Recession is a clever pun, a play on words, an attempt to compare the current recession with the economic woes of the Great Depression, which, at least in the U.S., began with the stock market crash of 1929, and ended during World War II.
I don't think it would be right to call great recession a "common term" – it's more like an easy rhyme. Have a look for yourself to see how "common" the expression is.
Given that the nation's economy still hasn't completely pulled out of its doldrums, I think it's too early to say how historians will officially label these lean economic times. There was the S&L crisis of the 80's and 90's, and the dot-com bubble in the late 1990's – those are pretty much established terms. If I had to venture a capital guess on what this current recession might be known as in the future, I might speculate on the Mortgage Crisis, since that seems to be the most-pointed-to trigger event. The Great Recession might turn out to be an enduring historical name, but it also wouldn't surprise me if the "Great Recession" label was eventually shelved as a cute nickname, one that might be applied to some other global recession, sometime in the future.
As Jim pointed out, a Wikipedia article links to the term Great Recession, but I'm not convinced that name will have stuck 10 years from now. The name of an historical event can evolve as we view it more retrospectively. There was a time when World War I was called The Great War; it didn't make sense to call it World War I before there was a second world war, and it didn't make sense to call it "The Great War" after World War II. WWI was even known for a time as "the war to end all wars," but that nickname didn't stick for very long either, for rather obvious reasons.