Phony Benoni: OK, this gets complicated.
Once upon a time--around 1935 or so--there was a song called "Moon Over Miami". It became popular enough to turn into a 1941 film.
Many years later Denny's, a US restaurant chain which is open 24/7, needed a new early morning snack. They came up with a sandwich made of scrambled eggs and ham, and having no shame named it "Moons Over My Hammy".
Why moons, I don't know. I can see eggs over easy resembling moons, but scrambled eggs?
At any rate, when this game played by someone named Hammie hit the database, somebody else who probably stays up all night at Denny's thinking up puns noticed the obvious application.
As for the game, a better pun might have been Slaughterhouse Five.