Title Rank is a gameplay mechanic introduced in Total War: Three Kingdoms.
Overview
Aside from the Faction Rank owned by faction leader. Each character in player's faction has their own Title Rank assigned by the player. Higher rank grants better salary (upkeep cost) which increases satisfaction for the character that received it. Other than being a ceremonial reward to unsatisfied heroes and their lust for fame, Title Rank doesn't modify any battle/campaign related stats.
How does it work
Each character has a title rank of their own, regardless of any other role you grant them in your faction court, which entitles them to a specific salary and brings them a certain level of satisfaction. This is viewable in the character panel, next to the character's age and satisfaction rating.
Characters will desire a higher office as they level up which, if unfulfilled, can damage their satisfaction. Promotion is therefore a principle method for improving their satisfaction. Higher ranks require you to pay higher salaries each turn.