What is the name for someone who gives his subordinates a morale boost?

Solution 1:

In terms of giving a morale boost, one could refer to an inspirational or totemic leader. As a noun, a leader could simply be described as an inspiration, although this is a broad term that can refer to any inspiration. If someone gains power/morale from being supported by their troop, they can be said to have been rallied by the troop, and in return they can rally their troop. As you suggested, the leader could also be motivated by their troops, or motivate their troops.

In a civilian as opposed to a military context, there are all sorts of positive adjectives one might wish to assign a good leader who boosts their people's morale. Some of these could be competent, charismatic, and charming. A great leader may become famous and/or celebrated.

Solution 2:

Besides the previously-mentioned inspiring, motivating, and charismatic, consider

• compelling, "forceful". Example: Under her compelling leadership they succeeded where none had before.
• influential, "Having considerable influence". Example: He was influential in leading the team to success.
• stimulating, "Having a manner that stimulates (encourages into action; arouses... to functional activity)". Example: Under her stimulating leadership, they found a new explanation.

A literal term for "someone who gains power from being supported by their troop" might be symbiont, a noun for a participant in symbiosis, "a relationship with mutual benefit between individuals or organisms". Of such a leader, one might use terms energised ("invigorated, made energetic; supplied with energy") if the leader feels inspired by the troops, or idolized or trusted if the leader gains political or military power via loyalty of troops.