Found this on Yahoo:
In John Wayne's own words, "There've been a lot of stories about how I got to be called Duke. One was that I played the part of a duke in a school play, which I never did. Sometimes, they even said I was descended from royalty! It was all a lot of rubbish. Hell, the truth is that I was named after a dog!"
John Wayne was born Marion Michael Morrison in Winterset, Iowa. When young Marion was six, the family moved to California, eventually settling in Glendale. Marion delivered newspapers in the morning with his trusty Airedale, Duke. The locale firemen called them "Big Duke" and "Little Duke."
Marion later accepted a full scholarship to play football at the University of Southern California. In the summer of 1926, head coach Howard Jones fixed Duke up with a job as an assistant prop man on the set of a John Ford movie. The rest is history.