Barry spotted a 1943 trademark application for the term Jeepmobile. The application may have been denied, as the USPTO does not have a record of that term being awarded a registered trademark status.
So, why trademark the term? My guess is that W-O had noticed that the term was, at times, being used to describe the jeep. For example, the third paragraph in this 1941 article that appeared in a variety of newspapers describes the jeep as “jeep-mobiles” or “blitz buggies”:
The application claims the term was first used by the company on March 01, 1943, which likely means it should appear in some ad some where, but I couldn’t find any ad with that term.
Perhaps securing the term was a defensive measure against others using it (especially Ford)? We’ll likely never know.
After the war, the term pops up several times in newspaper articles as well. So, in some form, the term was used by the public most likely in casual conversation rather than as a formal description by W-O.