In reverence to Thespus, actors throughout western history have been referred to as thespians.
In theatrical myth (or superstition), Thespus is said to exist now as a mischievous spirit, and when things go wrong in performances it is often blamed on his ghostly intervention. Like many superstitions, this belief ranges in different cases from being considered a humorous legend to being taken very seriously, with various charms and rituals being employed to either invite his approval or defend against him.
In theatre and acting craft, there is a minor school of thought known as "anti-thespian," which posits that it is inappropriate or artistically flawed to assume a character other than yourself. It is not a moral objection, but more a suggestion that actors should not make any effort to disguise or distract from who they are (in theory, because stories themselves are what matter, not the distraction of creating false depictions of people.)