The riddle
What Do You Call Cheese That Is Not Yours?
When two words melt together
English speakers often fuse a t and a y sound into "ch" when words meet. Wikipedia's article on yod-coalescence says the merging can happen across word boundaries and gives "gotcha" for "got you" as an example. "Not your" follows the same path and comes out close to "notch-er". Nacho ends in "oh" and not "er", so the match is near and not exact, but the first half is almost identical.
Who named the snack
Wikipedia traces nachos to the city of Piedras Negras, in the Mexican state of Coahuila, just across the border from Eagle Pass, Texas. In 1943 a maître d' named Ignacio Anaya, working at a restaurant called the Victory Club, cut fried tortillas into triangles, added cheese and sliced jalapeño peppers, and heated them. He called the dish "Nacho's Special". Nacho is a common nickname for Ignacio.
The name before the dish
So the word nacho began as a person's nickname and was borrowed for the food. Wiktionary adds that the singular nacho, a single chip, is a back-formation from nachos. The first known appearance of the word "nachos" in English dates to 1949, according to Wikipedia.
A fast-talk challenge
Say "not your cheese" at a normal talking speed, then very slowly with a pause between the words. The pun fades the moment the t and the y are pulled apart. It is a handy way to show a group how much of English is glued together in speech. Worth trying next: when does a joke become a dad joke.