First of all you need to understand that Count Basie was the man. In the 1920s he was living in Harlem playing hot jazz at shows and vaudeville gigs. He moved around he toured, he started to build a career. But his first recordings happened in 1936. Radio is how he got there.
In 1929 he became a pianist for Bennie Moten. Moten was great, the former leader of 'Bennie Moten's Radio Orchestra" but during a 1935 tonsillectomy Moten died of a freak heart attack. Basie took over as bandleader. The band was the Barons of Rhythm. Moten's nephew was a pseudo bandleader and led the band to a gig doing radio broadcasts in a tiny jazz joint called Club Reno in Kansas City. That radio station was 1550 W9XBY.W9XBY was one of four experimental high fidelity licensed by the FRC in 1933. These stations were were permitted to be 20 KHz wide instead of the standard 10 kHz. they occupied 1530, 1570, and 1550. These stations were:
W1XBS - Waterbury, CT
W2XR - Long Island City, NY
W9XBY - Kansas City, MO
W6XAI - Bakersfield, CA
W9XBY went on air for the first time in December if 1934. In 1937 W9XBY got the calls KXBY-AM. But long before that happened, the high power, high fidelity signals were booming across the plains. It allowed none other than John Hammond to hear nightly broadcasts from Count Basie's nightly shows all they in New York City. (I know this isn't apocryphal as Mezz Mezzerow makes the same claim in his own bio) This is crucial because at the time not only was Hammond a writer for Downbeat but also an A&R man for Columbia Records. Basie got a booking agent and a deal with Decca.
In one article Basie attributed his nickname to these broadcasts "One night the announcer called me over to the microphone for those usual few words of introduction. He commented that Bill Basie was a rather ordinary name and that there were a couple of well known band leaders named Earl and Duke. Then he said, 'Bill, I think I'll call you Count Basie from now on." The band became Count Basie and the Cherry Blossoms and they became the the house band at Club Reno in the summer of 1935. But this was the era of hot jazz, and Basie was at his creative peak as a man of le jazz hot, and swing.
Basie outlasted KXBY-AM. After Basie blew town Jesse Prices Big band played the gig, then George E. Lee. The station began carrying Mutual Network programming at night and dropped the Club Reno sponsored program. In 1942 due to ownership tumult the FCC revoked their license. They held a hearing and nobody even showed up. The Club Reno was later re-named the House of Swing. Today it's location at 602 E. 12th Street is now occupied by a parking lot.
*image from qcwa.org