The original Jeep went into production in 1941 and was used exclusively by the United States Military during World War II. It's hard to say where the name "Jeep" came from, although many believe that it's a slur on the military designation "GP", or "Government Purposes".
Another popular theory is that it was named after a character from the Popeye comic strip called "Eugene the Jeep". Eugene the Jeep was Popeye's pet companion in the late 30s/early 40s, and described as "small, able to move between dimensions and could solve seemingly impossible problems."