If Dooku wasn't a Sith the tule of two Sith would be broken. But since you're stubborn here's an excerpt from Dooku's databank entry on the offficial site.
After his departure from the Jedi order, Dooku was seduced to the dark side by Darth Sidious, the Dark Lord of the Sith. By Sith tradition, Dooku adopted the name Darth Tyranus and added deceit and treachery to his already formidable array of weapons.
And another one
With the Clone Wars in full effect, Count Dooku -- now Darth Tyranus -- fully embraced the ancient teachings of the Sith.
Have u ever heard of EU? Comics? Books? Before you make a statement you should inform, because they both had several apprentices: Hethrir, Vost Tyne, Lumiya and Mara Jade. All were dark jedi, no Sith because they were trained in the force but not in Sith teachings. I think you should watch all the movies again, because you obviously missed the whole point.
Something else, Darth would be familiar to fans, but Uthar Wynn didn't have Darth in his name and he was a Sith too.