I always heard that the name Jeep for the military vehicle came from the Popeye comic strip.
The word jeep, however, was used as early as 1914 by US Army mechanics assigned to test new vehicles. In 1937, tractors which were supplied by Minneapolis Moline to the US Army were called jeeps. A precursor of the Boeing B-17 Flying Fortress was also referred to as the jeep.
So "jeep" was around BEFORE either Popeye used it, OR AMC.
I suspected as much, since in Popeye, Eugene is referred to as THE Jeep. Not just Jeep. So Segar must have heard it before then.
The whole debate reminds me of Alfred E. Neuman.
Mad artists have used him as their mascot, but he is unquestionably MUCH older. And Mad artists were explicit in admitting that they copied the image.
Earliest known references are from 1894.
But I'm pretty sure that Mad "owns" the image today. I could be wrong.
Wikipedia is unclear.