Count Dooku is only called a Count দ্বারা most people because gained the শিরোনাম from his family. He is also called Darth Tyranus দ্বারা his master (Palpatine)
My guess ( Im a moderate-smart) as far as knowing the তারকা 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 অথবা 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 ব্যক্ত very much although palpatine makes up a story about darth tyranus in episode three