Duke (Hat) refers to a tall teardrop, cowboy hat with an oversized brim. The Duke's shape was one of the favorites of John Wayne, an American actor who had mostly filmed cowboy films.
When people mention John Wayne's name, most of the people who watched him on his cowboy films remember him wearing this style of cowboy hat.
Author's Note: Visit Limpia Creek Hat's website http://www.limpiacreekhats.com.
They have available Hats made in celebration of the 100th birthday of the legendary John Wayne.