There are plenty of theories but not much agreement on the origin of the name. One thing is for certain though - "jeeps" became a fixture in the U.S. Army in 1941 when the first 1/4 Ton 4x4 Truck G503, manufactured by the Willys Overland Motor Company, was purchased for use in WWII.
This "general purpose" or "GP" vehicle was used as everything from an ambulance to a weapons carrier in every theater of operation during WWII.
The WWII Jeep was built between 1941 and 1945 and it served with distinction in every theatre of operation. Army Jeeps were surplused after the war and have become a fixture in popular American culture.
The Jeep timeline: