When the boats arrive to save everyone at Radio Rock their fans cry out the names of the DJs as they pull them from the ocean. How would they know what any of them look like?
If you watch the deleted scenes (all 45 minutes of them!), you will see two scenes about "Magnificent Monday," which is when 200 "lucky contest winners" get to come aboard the Radio Rock for a day. That explains how the fans would recognize their beloved DJs (as well as the young black guy, Harold, who's just a tech guy).
Also, the pirate ships of the 1960's operated as normal businesses, and photos of the DJs were sent out to fans, appeared in newspapers etc.
