I never thought about this but perhaps Germans did not see it as a world war or preferred not to think of it as such. Or, maybe WW2 only became a popular term in most places after the war was over?
Surprisingly, the answer already exists on English.se:
OED says that the Manchester Guardian coined "World War No. 2" on 18 February 1919, "with reference to an imagined future war arising out of the social upheaval consequent upon the First World War (1914-18)."
Their next citation for "World War II" is Time Magazine on 11 September 1939.
So it seems that World War 2 (or variantly The Second World War) was always called by those names, at least in English speaking countries. The former seems the dominant usage in North America, and the second dominatn in the United Kingdom.
In Russia, the war has (I believe) always been called The Great Patriotic War, at least in regards to after the invasion of the Soviet Union by the Germans on June 22, 1941.