In "The Sponge Who Could Fly," SpongeBob accidentally cause accidents for Old Man Jenkins, causing him to change his profession, from Farmer to Sailor, and then Cannonball, where he shoots SpongeBob down.
His name is a character name used in various episodes as the running gag. The name was originally applied to the elderly green fish in the image to the right, who appears commonly throughout the series, but in other episodes, the name "Old Man Jenkins" has been used for completely different characters, such as a green fish in a wheel chair and a blue fish in overalls. They are always elderly fish. His first name is unknown.
The reason for so many different versions of Old Man Jenkins has never been explained. However, there could just be different elderly fish with the name Old Man Jenkins, because Jenkins is a common name.
One of these Jenkins died in "Friend or Foe" due to K.O. food poisoning.
This character's name is commonly used for gags in the show. This may also explain why there are different versions of Old Man Jenkins.
There is also an Old Man Jenkins in the console version of Creature From the Krusty Krab. He seems to resemble the cannonball Old Man Jenkins the most.