Actually, you would have to do a directed search to find anyone on CP and most of the other sites. They contractually prohibit them from disclosing their personal sites and advertising them specifically to avoid theft of services (ie, stealing clients and name lists).
Twice through the years I located (once by accident) psychics who also worked for major lines and in both cases was refused service when asked if I knew they also worked for Keen and CP. That's honest, to give them credit. I have been asked a few times to "stay in touch" meaning call back to CP when it was clear the psychic would have liked to have had contact outside the company, none ever crossed that professional line.