He is an alter-ego of Patrick who wears doctor's equipment. He wears doctor clothes in "The Splinter," but he appears in his normal clothing in "Suds".
Role in series
He tries to cure SpongeBob from the eponymous disease. He tries many unusual methods like spreading Sea-Nut Butter on the soles of SpongeBob's feet and sandwiching them with slices of bread, taking out his tooth attached to a string out by closing the door on said string, and persistently ripping a bandage off of his back, but nothing he does helps except for plunging up his holes.
SpongeBob Goes to the Doctor
The role Doctor Patrick has in "Suds" is the same role in this book.
SpongeBob goes to Doctor Patrick to help against his splinter. At first, Patrick disregards the treatment by randomly putting SpongeBob's foot in his mouth. However, Patrick eventually draws attention to the wood lodged into SpongeBob's thumb afterwards, though only makes matters worse by hammering the splinter and covering the wound in garbage, causing his thumb to swell up, turn purple, and produce pus.
The roles of doctor and patient between Patrick and SpongeBob respectively are reversed in the episode "Suction Cup Symphony."
Both of Doctor Patrick's treatments in his two appearances involve SpongeBob being barefoot.
In "Suds," Sandy threatens to have Doctor Patrick arrested for impersonating a doctor, and she is right. It is illegal to impersonate a doctor, as it requires doctor's insurance and a college bachelor's degree.