On Tuesday, Clear Channel — by far the largest operator of radio stations in the United States — renamed itself iHeartMedia, in recognition of what Robert Pittman, the company’s chief executive, says is how thoroughly the iHeartRadio franchise has become incorporated into virtually everything Clear Channel does. Across the country, listeners to Clear Channel’s various radio stations, such as the popular Top 40 outlets Z100 in New York (WHTZ, 100.3 FM) and KIIS in Los Angeles (102.7 FM), can scarcely listen to an hour of music without disc jockeys encouraging them to try the app and interact with them on iHeart-themed websites and social-media channels — making iHeartRadio a valuable national brand in what is a largely local radio business.