WWI was originally called The Great War or The World War. It was the largest war, in terms of participants, in recent history. Especially as the casualties began to mount and trench warfare set in. Hundreds of thousands of soldiers died at the Battle of the Somme, far more than ever fathomed.
The Oxford English Dictionary quotes that the Manchester Guardian used the term "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, ten days after the Blitzkrieg in Poland.
The phrase Second World War was always used in conjunction with the war itself. It was also used in reference to a forthcoming conflict in light of the harsh terms of the Treat of Versailles and the rise of fascism in Germany.