Before the Second World War, WW1 was known as the Great War. Why wasn't WW2 named the second great war? Also, on a related note, when was WW1 renamed?
In regards to when was The First World War/WW1 named as such the German scientist Ernst Haeckel called the First World War the "first world war" back in September, 1914.
The British Army officer and war correspondent Charles à Court Repington published a book in 1920 called "The First World War, 1914-1918".
https://archive.org/details/firstworldwar19102repiuoft
The term "Great War" for the First World War was used in October, 1914 in Maclean’s Magazine. "Some wars name themselves...This is the Great War."
http://www.wordorigins.org/index.php/more/581/
So the term "First World War" seems to predate the term "Great War" for the First World War.
As to why WW2 wasn't named "The Second Great War" I wasn't able to find anything that said why WW2/Second World War was chosen.