It was probably named after Eugene the Jeep, a character out of Elzie Crisler Segar's comic strip Popeye!

Olive Oyl received this small yellow creature from her Uncle Ben on March 3, 1936, about four years before the US Army started testing the new quarter-ton utility vehicle which would eventually be called the Jeep.

Eugene could walk through walls, appear out of nowhere and pretty much go anywhere he wanted.

The new vehicle's go-anywhere, do-anything capabilities reminded the soldiers of this character and so dubbed the new vehicle a "Jeep"!