Count Dooku is only called a Count oleh most people because gained the judul from his family. He is also called Darth Tyranus oleh his master (Palpatine)
My guess ( Im a moderate-smart) as far as knowing the bintang Wars facts of life. But my guess is because he was involved with the Sepratists. He was Darth Tyranus. But when he joined the Sepratists movement, my guess is he wasnt fully for the Sith atau the Jedi. Cause thats what the Sepratists are. In our world they would be Independents. IDK, best guess.
yea as a normal person he is a COUNT but he does have a sith name that isnt berkata very much although palpatine makes up a story about darth tyranus in episode three