The name Jeep is a protected trademark owned by Chrysler.

It definitely came from the Popeye comic book and cartoon character which debuted in 1936.

"A Jeep is an animal living in a three dimensional world—in this case our world—but really belonging to a fourth dimensional world. Here's what happened. A number of Jeep life cells were somehow forced through the dimensional barrier into our world. They combined at a favorable time with free life cells of the African Hooey Hound. The electrical vibrations of the Hooey Hound cell and the foreign cell were the same. They were kindred cells. In fact, all things are, to some extent, relative, whether they be of this or some other world, now you see. The extremely favorable conditions of germination in Africa caused a fusion of these life cells. So the uniting of kindred cells caused a transmutation. The result, a mysterious strange animal."