I was wondering what would happen if a station hired a talent who wanted to keep his own name.
That's what most people do. Of course one way to formalize it is to join AFTRA and make it your union name. But if you work for a Froggy station, they tell you to take a name with a frog reference.
Radio is an itinerant business, with talent moving from one station to another, often in the same market. So when an established talent moves to a new station in the same market, it's possible that he might want to bring his listener base along with him by keeping his name from the previous station.
There are lots of examples of that. Scott Shannon is a guy who's used that name at three different stations in NYC. On the other hand I know of three different people who used the stage name of Johnny Dark.