The excellently named u/lord_mayor_of_reddit answered a similar question, "The Great War was later renamed World War I. When did this change happen? Was WWII called such from the start?" here: https://www.reddit.com/r/AskHistorians/comments/4vnv4j/comment/d60dilh/?utm_source=share&utm_medium=web2x&context=3

While more can always be said, you might be interested in this previous answer on how the Second World War became known as such.