It is simply to create the illusion that all of the stations aren't owned by one company.
Hate to dismantle your soapbox here, but that's wrong in pretty much every case I've seen.
Back in the day, program directors did not want traffic people using the same name on the competition (and that's still true today, where these traffic reporters are shared among competing clusters).
An example, admittedly from the mid-1990s:
A large market news/talk station had a competing talk station in the market. Metro's reporter used separate names on each station. The news/talk parent company (yes, the "evil" Clear Channel) ended up buying the competitor. As soon as the stations were under the same ownership, the Metro reporter started using the same name on both stations.
Though it's not what it was, there is still competition...and the Clear Channel PD/OM doesn't want his or her Metro(/Total Traffic) reporter with the same name on the CBS or Salem station(s).
Some of it was ratings confusion in the diary era, which is obviously gone in PPM markets like LA.
But even within clusters, there are still issues of stations wanting traffic reporter names sound like they're in the same lifestyle group as the station.