Gardner actually hand-picked Burr for the role: he hadn't liked any of the actors that the network had brought in to play PM, but Fred McMurray was leading. Burr, who had played the bad guy in several films, was brought in to read for the role of District Attorney Hamilton Burger. When watching Burr's screen test, Gardner stood up, pointed at the screen, and said "That's him! That's Perry Mason!" His PM novels during and after the TV show were obviously written with Burr in mind, as Mason's physical description and speech patterns were changed to more closely match Burr's.
You're thinking of the radio soap opera Edge of Night, which included Perry, Della, and Paul as regular characters. When they made the transition to television in the 1950s, the series was split in two, with Perry, Della and Paul going to the Perry Mason series which was strictly episodic with no soap opera elements, and Edge of Night having those three characters renamed.