The short answer is no, though it’s hard to pinpoint precisely when the World War I and World War II—or First World War and Second World War—monikers arose. During World War I, of course, nobody knew that a second global conflict would follow closely on the heels of the first, so there was no need to distinguish it as the first of its kind.
After initially referring to the “European War,” U.S. newspapers adopted “World War” once America entered the confrontation in 1917. On the other side of the Atlantic, meanwhile, Britons preferred “Great War” until the 1940s—with the notable exception of Winston Churchill, who reminisced about the “World War” in the 1927 volume of his memoir The World Crisis.
“World War II,” on the other hand, first appeared in print all the way back in February 1919, when a Manchester Guardian article used the term much in the way people today predict a hypothetical “World War III.” But it was Franklin D. Roosevelt who in 1941 would publicly label the conflict the “Second World War,” and his fellow Americans quickly followed suit. (In Britain, it remained simply “the War” until the late 1940s.)
While Roosevelt may have helped popularize the name, it seems he wasn’t entirely satisfied with it. In 1942 he asked the public to propose alternate appellations, and over the next few weeks the War Department received 15,000 submissions ranging from “the War for Civilization” to “the War Against Enslavement.” Neither these nor Roosevelt’s own choice—“the Survival War”—had staying power. “World War II” and “Second World War” it was—and, as a result, “I” or “First” was appended to the clash that preceded it.