I can't help but feel what you're talking about here is "high impression management" related to personality.

There are two types of "high impression management". One is related to conscientiousness as a positive aspect to one's personality. Then, there is a negative, deceptive aspect associated with Machiavellianism. This aspect of personality is closely associated with the Dark Triad of personality and the Dark Tetrad. Both these aspects of personality, Dark Triad and Dark Tetrad, have been associated with people studying Business degrees in academic settings, according to a research study.

And I don't think you need to be "fake" to be an effective leader. I think you need to be human and have a capacity for strong interpersonal skills paired with the ability to relate to others compassionately.