They were within a couple of blocks of each other when I knew them. They both had windows to Market Street, but Cochran's entrance was on Golden Gate.
Cochran's was taken over by Tony Annigoni and partners after they had taken over and then closed Palace Billiards. I believe Cochran's was rechristened "The Cue Club" and may have turned into Hollywood Billiards later. It now seems to have been turned into residential space, judging from Street View.
that's it... it was named Hollywood Billiards when I visited in 2001.