Narcissism was an obsessive admiration of oneself and one's appearances or abilities.
A parallel version of Davros called the Dalek Emperor a bloated narcissist on broadcast during the Last Great Time War. (AUDIO: Restoration of the Daleks) He was correct because the Emperor showed such conceit and vanity, even calling itself a god. (AUDIO: Homecoming; TV: The Parting of the Ways)
Morbius showed a degree of narcissism; as "the General", the walls of the War Room of his flagship was covered in mirrors so he could look on himself. (PROSE: Warmonger)
The Beast had a narcissistic personality, constantly exalting itself and its achievements and referring to itself by various grandiose epithets, including the third person. (TV: The Impossible Planet/The Satan Pit)