The Big Mac supplied the name for McDonald's 1968 packaging-and-advertising character, Officer Big Mac.
Officer Big Mac was one of the characters used in McDonaldland advertising. His name and appearance connected him directly to the Big Mac sandwich, making the product part of the fictional character system rather than merely a menu item. The character was depicted as a police officer and appeared alongside other McDonaldland figures.
The Big Mac itself was introduced nationally in the United States in 1968. Its distinctive three-part bun, two beef patties, special sauce, lettuce, cheese, pickles, and onions made it one of McDonald's most recognizable products. The product name therefore had a life in both menu branding and character branding.
Officer Big Mac is sometimes confused with Mayor McCheese because both were civic-style characters. The answer here is the sandwich whose name appears in Officer Big Mac's title: Big Mac.