The World Wars were not called "World War" initially. World War I was called Great War before it was popularly referred to as World War. It was called the Great War because it was literally greater than any War that had happened in the past. It was also known as "War to end Wars".
The term, World War I didn't come into existence before World War II because no one knew there was going to be another World War. The term World War appeared first in an article in 1919.
The major world wars were not originally called world wars. At the time, what is now called World War I, no one was expecting a second war so there was no need to designate it as the first. For many years, in fact, until the 1940’s, the British referred to World War I as the Great War. American newspapers initially referred to World War I as the “European War”, until America joined the war in 1917.
History.com says the term World War II first appeared in 1919 in an article “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.”