All the Michigan places listed below are villages and they have the same name as other established places inside the United States.
Nashville, Michigan was a nameless plot of land that was often privately owned until 1869 when Garaudus Nash suggested the village should be named after him.
Nashville, Tennessee had been established in 1805 and was named after Frances Nash.
Akron, Michigan and Akron, Ohio
Brooklyn, Michigan and Brooklyn, New York
Camden, Michigan and Camden, California
Nashville, Michigan and Nashville, Tennessee.