Duke Yukthomas Féyêdêmuffin (or the Duke as he likes to be called), is a character played by SpongeBob, seen in the episode "Summer Job." The Duke orders beans on toast, which is not on the menu in the Krusty Krab.
The Duke wears a navy blue suit, a black top hat with a light purple stripe, black shoes and has a mustache with a small beard. He looks very similar to SpongeBob. Mr. Krabs says that the Duke is one of his "regulars" and scolds Mrs. Puff for yelling at him. However, SpongeBob reveals himself as the Duke directly afterwards.
When SpongeBob is teaching Mrs. Puff how to deal with manning the register at the Krusty Krab, SpongeBob disguises himself as the Duke. When he orders beans on toast, Mrs. Puff says it's coming right up, but he then responds by saying beans on toast is not on the menu. Mrs. Puff starts shouting at him and Mr. Krabs comes out and says that the Duke is one of his regulars. Mr. Krabs then tells Mrs. Puff not to let it happen again.
Since SpongeBob was in a costume, maybe there actually was a customer named Duke that was a regular, and SpongeBob was disguising himself as them.