The McDonald's product that inspired Mayor McCheese's name was the cheeseburger.
Mayor McCheese was a McDonaldland character with a large cheeseburger for a head. He appeared in advertising alongside Ronald McDonald and other costumed figures during the brand's heavily character-driven campaigns of the 1970s and 1980s.
The character's design made the connection to McDonald's food especially direct: his head represented a cheeseburger, while his formal mayoral clothing gave the character a civic role in the fictional McDonaldland setting. Mayor McCheese is distinct from the Hamburglar, whose identity centered on stealing hamburgers.