You generally cannot trademark a single word like Trump when it has other meanings and found in the dictionary. For example, Apple has trademarked "Apple" but they only own the word when it is used in combination with one of Apple's products, such as "Apple Computer" or "Apple cellphone".
That said, I would not be surprised if the radio station got permission to use Trump's name as part of the station's identifier. Do remember when the Disney Corporation was suing everyone and everything that used Mickey, Mouse, mouse images, or mouse ears as a logo or company name. If you had a bar named "Mickey's" because your name was Mickey Doyle then you could expect a visit from Disney attorneys demanding that you change the name or be sued by a corporation with unlimited resources. No reason to not get permission, and particularly if they are also using his image as another answer says.