For example, did Ivan the Terrible know he was feared (terrible in the sense of causing terror), and relish the name? How did Pepin the Short feel about his style, if he even knew? Etc.
I am not sure what you mean by "style." Elizabeth I (The Virgin Queen) and Louis XIV are examples of monarchs who carefully crafted a persona in which performance and politics were intertwined. See Strong's The Cult of Elizabeth and Burke's The Fabrication of Louis XIV.