Unless I have misunderstood something even "general purpose" was also just a nickname. "G" stands for government, "P" represents 80 inch wheelbase, and "W" stood for Willys. The Ford GPW wasn't built until after Willy's couldn't keep up with the war demand. The famous picture of where the Jeep drove up the stairs and was publicly called "JEEP" on February 19, 1941 was before the Ford GPW came along.
The other common one I hear is that the name came from Eugene the jeep from Popeye. "Jeep Jeep" first appeared March 16, 1936. So at this point we can definitely rule out the jeep came from "gp, general purpose." As much as I love Popeye, I don't think this is where it came from either. We need to go back further in time.
In WW1 new recruits that had not seen battle were sometimes called "jeeps." The mechanics and others at the time also used the term for untested vehicles. There were certainly plenty of people that had served in both WW1 and WW2. It would come as no surprise if the term "Jeep" just carried over.
Regardless of where the name came from, our beloved Jeeps still started out kicking a$$ as a WW2 vehicle. ?