They often have a mix of their call sign and another brand. The conglomerates have a few brands like The River (something for everyone is nothing at all). Local stations sometimes emphasize the call sign or they have something else, like 88.5 in Atlanta is "Album 88", or WRAS.

Who knows why we landed on our system of 3 and 4 letter call signs, but we did. Plenty of stations use them only when they have to: in the top of the hour legal ID, which is "<call sign> <city>," such as WZZQ Terre Haute.

Branding was usually based on FCC callsigns. But not always... many people in the US grew up with some Z100 or morning crew brands too.

Other countries have similarly arbitrary brands based on either band spectrum or regulatory regimes - eg Channel 4 / Radio 4