When I first started in radio, you used air names for two reasons: First, because back then, there was almost no such thing as an “unlisted” number, and if you used your real name, you’d almost certainly get crank calls at home.
Secondly, it was just kind of the style for DJs to have a “friendly” first name, and a one-syllable second name, so you had “Mickey Jay”, “Bobby Gaye” (he’s still working under that name, believe it or not), and the like. A lot of times, you’d also have somebody try for an alliterative effect (“Wee Windy Winslow”, “Slammin’ Sammy Salmon” etc.)
In my own case, I just never liked being recognized in public. I always hated it when somebody would say “You sound familiar; have you been on the radio?”