It depends how you define "World." The war which commenced in 1939 was only between European states, while the two most industrially powerful countries on the globe (USA and Soviet Union) were not at war. It only becomes an actual world war in 1941. It could be rationally argued that if the war had ended before 1941, before the USA and SU got involved, then it would just have been called the European War, or the Great Nazi War, or the Anglo-Franco-German War or something similar. It is difficult to see why a war which leaves out the two most powerful countries on Earth could in any real sense be called a "world" war. (And I am writing this as a European.) Still, the war has to be called something, and once it became a world war in 1941 then the name could retrospectively be applied to the fighting which preceded it.