From the September 1, 2018, History "Were they always called World War I and World War II?" by Elizabeth Nix.
We call it World War II in the United States. England refers to it as the Second World War.
It is hard to pinpont exactly when the names came into use. During World War I, of course, no one knew there was going to be a second one, so there was no reason to distinguish it. Often, it was referred to as the Great War.
After initially calling the first one, the European War, U.S. newspapers adopted World War after the country entered the war.
The term "World War II" first appeared in print all the way back to February 1919, when a Manchester Guardian article used the term, much in the same way people today refer to a World War III. But in 1941, it was President Franklin D. Roosevelt who labeled the conflict the "Second World War."
Even so, in 1942, he asked for name submissions from the public and over the next several weeks, the War Department received 15,000 names ranging from "The War for Civilization" to "The War Against Enslavement."
However, it was World War II and The Second World War that stuck.
Now You Know. --GreGen