Face memory, including the ability to recall a person's name, is of major importance in social contexts. Like many other memory functions, it may rely on sleep. We investigated whether targeted memory reactivation during sleep could improve associative and perceptual aspects of face memory. Participants studied 80 face-name pairs, and then a subset of spoken names with associated background music was presented unobtrusively during a daytime nap. This manipulation preferentially improved name recall and face recognition for those reactivated face-name pairs, as modulated by two factors related to sleep quality; memory benefits were positively correlated with the duration of stage N3 sleep (slow-wave sleep) and negatively correlated with measures of sleep disruption. We conclude that (a) reactivation of specific face-name memories during sleep can strengthen these associations and the constituent memories, and that (b) the effectiveness of this reactivation depends on uninterrupted N3 sleep.