I found this article by a head of IT at Oxford who also is a member of its English Language and Literature faculty and the "Reader in E-learning and Digital Libraries." (Oxford seems AWESOME.) He discusses the debate over what to call the war as it was happening- usually between The Great War and The World War- and mentions that the war was first called The First World War in 1920.

What's most interesting about his piece is that he includes a link to a resource that I would never have thought of- Google Books Ngram, which searches the books in Google's databases (and there are a LOT of them) and tracks key words over time. Here is the Ngram Viewer which he made for the terms World War I (and the alternate spelling World War One), The Great War, and The First World War.

Overall, the impression from the chart is that the term The Great War was in by far the greatest usage from the end of that war to the end of the 1930s, and that immediately after the start of WWII the term World War I (and to a lesser extent the First World War) climbed steadily and drastically in use, peaking in the decade from about 1945-1955. There seems to have been a slight use of the term First World War prior to 1939, but it was not the common usage.

A few caveats:

• This doesn't normalize the data PER book/article/report/etc written on the subject of WWI. It is very possible that the peak in usage of the term World War I in literature in the late 40s and early 50s is due to an increased discussion of the war at that stage, and that the decline after that is simply due to the war being less of a topic of discussion. It's also probable that the steep decline in the 21st century is due to the fact that the books came out after Google Books did its major scanning effort, which has slowed over time.
• I can't figure out whether the numbers used are based on numbers of BOOKS using the term or the amount the term is used AT ALL, even in the same book. This could skew things one way or the other, but not necessarily.
• I was worried that the spike in the late 40s-early 50s was due to Google Books highlighting/isolating "World War I" from "World War II" and just cutting off the last I. From the checking I did, this doesn't seem to be the case. However, I was also super confused at why the term "World War I" was used at all prior to 1939, and while I could accept a few usages, even the relatively few indicated by the Ngram Viewer seemed way too many. Most of them are in fact false positives- either books/reports that were issued post-WWII were mistakenly marked as being from before 1939, book titles were changed when they were reprinted, or Google Books highlighted "World War, I..." (as in "during the World War, I was a private") as the phrase World War I.

However, despite these caveats, I think that the conclusions which are drawn by and large here are really interesting and seem reliable and indicative of the real trends.