Simons is right on both counts. Eugene the Jeep did grace a 1930s cartoon, "Popeye the Sailor," and was a cute little character who went around saying, "Jeep, Jeep!" in reply to anything said to him.
Simon is equally correct in his definition of the quarter-ton vehicle that the Army labeled a quarter-ton GP truck in 1940 (there is a famous picture of one climbing the steps to the Capitol).
The only added information I am able to offer comes from a knowledge of the times and the usual way of GIs to invent acronyms--nicknames--for just about everything.
GP simply had to become "Jeep!" It was a natural! What else could it possibly be called at a time when just about everybody followed the adventures of Popeye, Olive Oyl, Bluto and of course, the Jeep?