The OED isn't a lot of use here, but its first two entries do suggest that the name may predate the war itself - which, considering how much of my youth was spent speculating about World War III, is perhaps not so surprising.
1919 Manch. Guardian 18 Feb. 10/2 (heading) World War No 2. 1939 Time 11 Sept. 38/1 Some of the diplomatic juggling which last week ended in World War II was old-fashioned international jockeying for power. Ibid. 18 Sept. 10/2 Exports of arms, munitions and related materials in World War I amounted..to only 25% of total exports to the Allies.