Why is George Jones called the Possum, and who gave that name?  

Hello, I searched the internet. This is what I found. Vince Gills called him the Possum at the end of his video, "One More Last Chance", as he is leaving the golf course on a John Deere tractor and George Jones arrives at the golf course on a John deere lawnmower. I hope that this answers your question. You can check it out at http://en.wikipedia.org/wiki/George_Jones

I don't know the name of a DJ or when the DJ named him that but because of Jones' close set eyes and upturned nose, he thought Jones looked like a possum.

I just watched Cribs on CMT and George himself said a DJ started calling him that b/c of the picture on the White Lightening album/single. The angle of the pic and his upturned nose made him resembled a possum. I've tried to find the pic he referred to but couldn't find anything. That's a pretty harsh nickname but I guess he's ok with it.