P.E.N.I.S., or Profile Exploring Networked Introductory System, is a tool for finding other characters based on their details. You can choose on a per-character basis which of your characters you want listed in P.E.N.I.S., (In the 'Preferences' category in the character editor page). By default, each character you create will be listed. They will also appear in the list regardless of being active.
For privacy reasons, other players can only contact you through the built-in messenger. Your SL/Player name will never be visible, only the character name will be shown. Once in the messenger, players can of course choose to give their SL contact details... Or could just put it in their character description if they wish to do so (Not recommended).