To be honest, I'm not entirely convinced that this qualifies as a nickname. But the phrase was certainly used to refer to him; so I would accept that it could be described as an epithet ("an adjective or phrase expressing a quality or attribute regarded as characteristic of the person or thing mentioned").
Wikipedia (never slow to suggest a nickname) only goes as far as to call it a "moniker": "He was called the 'prince of darkness', adding a patina of mystery to his public persona ... Writers began to refer to Davis as 'the Prince of Darkness' in liner notes of [his early] records ... and the moniker persisted."
Davis himself was happy enough with the 'moniker' to use it as the title of the opening track on his 1967 album Sorceror. (According to Wikipedia, he never played it in live performances.)
Miles Davis was known to be subject to mood swings and to have a rather short temper. But his nephew, Vince Wilbur Jr., stated on camera in 2019 however that "the Prince of Darkness thing" was not a true reflection of his uncle's character. According to Wilbur, Miles Davis was "sensitive ... sensitive to the music".
© Haydn Thompson 2021