For instance, I doubt that World War II was referred to as WW2 during its course, or that the 100 years war was known as the 100 years war while it was still going on. Were they just referred to as "The War", which I can't really see since I imagine that would get confusing really fast when multiple wars are ongoing, did they have boring names like "War of German aggression" or something along those lines?
World War 2 was referred to as "the second world war" pretty consistently. Being so close after WW1 (which was called "The Great War", "The War to End Wars", or "The World War") it was a pretty logical name.
In US history at least, wars are generally named after the country that they are fought in or given names that reflect their importance.