That Chrysler story about just enough essential parts sounds like an acronym that was made later. Chrysler did not build Jeeps during that time. The first jeeps were made by Willys-Overland, Ford and American Bantam.
Chrysler bought American Motors in 1987, who had bought out Kaiser in 1970. Kaiser bought Willys in 1953 and it became Kaiser-Jeep in 1963. The origin of the Jeep name and the trademark came from the original Willys company.
As an aside, teh Ford Motor Company produced GP vehicles and their documents state that G stood for Government Use. The P signified the wheelbase of the vehicle, in this case, 80 inches.
I have seen no documents that show the acronym JEEP.