When starting a new game, a save is made with the name of the world on embarking. If another world already exists by this name, it is overridden without any prompting.
I only discovered this when manually naming the world, but it may be possible (yet unlikely) for pure random chance to select a world name the same as an old one.
Create a new world with a specified name. Quit the game, start a new world, and give it the same name. The old save will be overridden with the new world without prompting.