A person with telepathy is called a telepath. Telepathy is a little like empathy, but empaths generally detect emotion and not thoughts.
For in-depth descriptions of the different telepathic systems, see their separate pages.
Psionics is a related concept (probably related to the word 'psychic'). It can encompass telepathy, empathy and other mental disciplines, as on Eodea. On Shade, by contrast, they use the terms "telepathy" and "psionics" interchangeably.
Discussion is crucial when roleplaying telepaths. All mind-reading requires the consent of both writers. Consent can be implicit - for example, if you wanted to, you could say in your character's biography "He's completely defenceless against telepaths, so go ahead".