These regiments have a name, they have one or more unique characters leading them and often have special rules or equipment that differentiate them from the norm.
All named models in a Regiments of Renown count as characters in the game. These characters cannot leave their unit (unless specified), but they do not use up any of the character slots from the army lists (unless specified).
If the characters have different equipment than the rest of the rank and file, this is clearly listed in the Equipment list. Note that, regardless of their Leadership value, these characters can never be an army’s General.