How did Count Basie get his name?

As quoted in Hear Me Talkin' to Ya: The Story of Jazz as Told by the Men who Made It (1966) by Nat Shapiro and Nat Hentoff: "Contrary to several conflicting stories, I got the name 'Count' right in Kansas City in 1936 while at the Reno Club. I was known as Bill Basie at that time. One night, while we were broadcasting, the announcer called me to the microphone for those usual few words of introduction. He commented that Bill Basie was a rather ordinary name, and further that there were a couple of well-known bandleaders named Earl Hines and Duke Ellington. Then he said, 'Bill, I think I'll call you Count Basie from now on. Is that all right with you?' I thought he was kidding, shrugged my shoulders and replied, 'OK.' Well that was the last time I was ever introduced as Bill Basie. From then on, it was Count Basie, and I never did lose that nickname. It's funny the way those things will stick."