Joe I was actually 'Wobbly Joe'. He had a cute little wobble in his front legs whenever he stood up. Turns out the wobble was indicative of quite a serious liver condition. Under the circumstances of Wobbly's sad end, it didn't feel right to name the next cat Joe II, but he just looked so much like him.
Joe III, by the way, is 'Driven to Joe' but I think his new owner's have renamed him Max. Lame.