I grew up in southern Minnesota and played Duck Duck Grey Duck as a kid. The first time I heard of Duck Duck Goose was when I moved away for college. When I first heard someone say Duck Duck Goose, I thought they were just making up a weird verse in the game.

We always played where each person tapped gets a different "Duck" so, "blue duck, orange duck, wet duck, baby duck, and so on" and then when the caller says "Grey Duck" then the chase is on. So in that version "goose" could just be one of the ducks called, so that's what I thought they were doing. It was much later that I learned that other folks didn't have any variation to the calls other than "goose" and "duck".