Dịch - Greek-English - ΚΑΤΑ ΤΟΝ ΔΑΙΜΟΝΑ ΕΑΥΤΟΥ

Here's what the wikipedia page says:

"Morrison's gravestone has a Greek inscription reading Κατὰ τον δαίμονα ἑαυτοῦ, in capital letters (ΚΑΤΑ ΤΟΝ ΔΑΙΜΟΝΑ ΕΑΥΤΟΥ). The meaning intended by the Morrison family when the inscription was selected is "True to his own spirit." Morrison's father either selected the phrase or drafted it himself. The literal meaning is "according to his own daimōn", an Ancient Greek word that implies a minor deity, attendant spirit, luck, fortune, "guiding star" and the like, with no negative or pejorative connotations."