Names such as "The Great War" or "The War to End all Wars" were pretty common. You've probably come across them from time to time if you've read about this.

However, the first person known to have called WW1 the "First World War" (albeit in German) was Ernst Haeckel, a German scientist.

"There is no doubt that the course and character of the feared "European war" ... will become the first world war in the full sense of the word."

http://books.google.com.au/books?id=ck6bXqt5shkC&pg=PA329&dq=The+Yale+book+of+quotations+ernst+haeckel+first+world+war&hl=en&sa=X&ei=eXE3U_fjJ9HrkwWP4oDIAw&ved=0CC8Q6AEwAA#v=onepage&q=The%20Yale%20book%20of%20quotations%20ernst%20haeckel%20first%20world%20war&f=false

Charles à Court Repington, a former British army officer, wrote a book in 1920 titled "The First World War".

https://archive.org/details/firstworldwar19100repi

The term "World War" itself had only entered English a few years before the First World War, probably from the German "Weltkrieg".

http://dictionary.reference.com/browse/world+war?s=t

Edit - added a quote and dictionary reference.