Let me explain: according to my children, 'cheese' is one of the words that is inherently funny*. Just as any sandwich can be improved by the addition of cheese,** any sentence can be made funnier by adding cheese. Thus your response to "John Cheese" is perfectly understandable.

*the others are: penguin, eyeball, underpants. They are funniest in combination. For example: Cheesy penguin eyeballs in your underpants!

** with the possible exception of peanut butter and jelly.