Brockport's Steve Pike said in a recent interview that he doesn't name captains. Rather than leading in tiers, he prefers to have his team lead in a circle. A circle he is a part of.
North Carolina's Anson Dorrance has his players call him "Anson" rather than "Coach." He believes it helps create the same sort of circle.
Famed social activist Dorthoy Day spent her life serving the poor. But rather than basking in the feelings of pride of her good works, she would guard against them:
"She guarded against spiritual pride, against the feeling of self-righteousness that might come over her because she was doing good works.
[...]
The sin of pride is around every corner, Day believed, and there are many corners even in a charity house. To serve others is to live under a great temptation." ~ David Brooks, The Road to CharacterThe one quality is humility. It requires a coach to hold two opposing ideas simultaneously: that he is the leader of the team, but not above it. He was chosen for a role that existed before him, and will exist after he is gone.
He serves unconditionally, fighting the need to be recognized for his service.
[This applies to athletes as well]