I am just curious that Dooku didn't ever reveal that he is Darth Tyranus. Why did Count Dooku hide his Sith identity as Darth Tyranus? Unlike Palpatine he revealed to Anakin that he is the Sith Lord. Was there a reason that Dooku did not reveal his Sith identity?
Firstly, if I recall correctly, Palpatine didn't actually tell Anakin he was a Sith Lord. He merely told Anakin that he knew the Dark Side of the Force, and Anakin put two and two together.
Secondly, Palpatine only did this as part of his convoluted master plan. He told the one Jedi he knew wouldn't just attack him on the spot, the Jedi he'd been manipulating from the very start. Anakin, rather than alerting the Council, told Mace Windu, who, rather than alerting the Council, tried to take Sidious down himself. This in turn allowed Sidious to finally turn Anakin to the Dark Side and gave him an excuse to execute Order 66 and disband the Senate, on the basis that the Jedi had just tried to launch a coup against him.
As for Dooku/Tyranus... prior to Attack of the Clones, he had the trust of the Jedi, to an extent. Revealing he was a Sith would have turned the Jedi against him; revealing he was the same Sith who gave Jango Fett his orders could potentially have unraveled the whole of Sidious' plan.
EDIT: As the OP noted in the comments, Dooku does of course reveal himself as a Sith at the end of the film, given that he fights with a red lightsaber and force lightning. It's been a while since I watched Attack of the Clones but to my knowledge, he only does this after being cornered by Obi-Wan and Anakin and having to defend himself. He intends to kill them, and given the way the fight was going until Yoda intervened, he likely would have succeeded, so he probably didn't think this would give him away in the long run. As it turns out, it did.
In short, Dooku didn't reveal he was a Sith until forced to, because he had nothing to gain by doing so.
The Sith...don't exactly have the best reputation in the galaxy.
Given that what is now Legends was considered canon at the time the films were made, I think we can reasonably draw on Legends resources to lay out what the galaxy as a whole thought of the Sith at the time.
The Galactic Republic's first real contact with the Sith was around 5,000 years before the films, and it was called the Great Hyperspace War. The war involved the invasion of the Republic by the descendants of Dark Jedi and the Sith species, and at one point Sith forces even landed on Coruscant itself.
After the Sith were driven back, there was a period of about a thousand years of occasional skirmishing, followed by another war around 4,000 years before the films, the Old Sith wars. Included in this period was the Jedi Civil War was fought between the Jedi and two of their most powerful members who had fallen to become Sith. Among other atrocities, this war saw the near-total desctruction of the city-planet of Taris.
The Great Galactic War was fought 3,600 years before the films. It involved the destruction of the Jedi temple on Coruscant by the Sith, the banishment of the Jedi from the Republic, and a lengthy cold war period, followed by the Galactic War, which virtually destroyed the Republic. The Sith Eternal Empire eventually collapsed from within, and the Republic was able to expand again.
2,000 years before the films, the New Sith Wars begin, and continue intermittently for around a thousand years, before the Sith are destroyed by one of their own, Darth Bane, who ushers in the Rule of Two era. The Rule of Two takes us up to the present.
All of these wars, conquests, and occupations by the Sith were marked by brutality, atrocities, and incalculable death and destruction.
So, what about Dooku?
Dooku's role was to build up the Separatist Alliance and the Confederacy of Independent Systems as a credible military and political power that could oppose the Republic. The Clone Wars showed us that many of the leaders of the Confederacy were every bit as idealistic as the Republican heroes; they believed what they were doing was right, that they were simply standing up for their rights against a corrupt government.
In this atmosphere, for Dooku to openly declare himself as a Sith named Darth Tyrannus would be tantamount to a present-day US politician declaring himself to be both a Royalist and a Nazi - instant political suicide.
Yes, he did reveal to the Jedi that he used a red lightsaber and Force lightning, both traditionally associated with the Sith, but it's important to note two things - First, that the only witnesses to these actions were Jedi, who his own people would not trust, and Second that while those powers are associated with the Sith, they're not exclusive to them. If it had come out that he used a red lightsaber and force lightning, he could easily claim that he only used them to distance himself from the corrupt Jedi. That's a far cry from directly declaring his allegiance to the Sith.
1. Major part of Sith Grand Plan was to blame Jedi for all
Dooku was well-known Jedi master in his time, and after that he become public face and leader of CIS. CIS of course acted ruthlessly, and in eyes of average Republic citizen Dooku became main villain. In effect, Jedi reputation was tarnished by this, it looked like they were fighting for both sides. Later, this helped Palpatine to push the story of "Jedi are taking over", and explain and justify Order 66. Dooku did leave Jedi Order prior to becoming head of CIS, but it is doubtful general public knew and understand that. After all, only twenty masters in entire history of Order left, it was expeted from Jedi to be Jedi all his life.
2. Jedi were kept in dark who created and paid for Clone Army
Jedi knew that man called Tyranus ordered Clone troops, but they didn't connect the dots until few months before Order 66. Only then (Clone Wars cartoon last season) did they found out that Tyranus is actually Darth Tyranus - Count Dooku. By that time it was too late to disband army created by Sith. If they found out earlier, they could have rejected this army, or at least got some time to discover Inhibitor chips used to execute Order 66.