Palpatine became Emperor after the Jedi attempted to arrest him and he issued Order 66. This also marked the close of the Clone Wars. As a result, the Republic was transformed into the Empire. The reason for the transformation was given by Palpatine in a speech to the Senate:
In order to ensure our security and continuing stability, the Republic will be reorganized into the first Galactic Empire, for a safe and secure society which I assure you will last for ten thousand years.
Since the Republic had just narrowly defeated the Confederacy and avoided a Jedi takeover (or so the public believed), the Senate thought that this transformation for their "security" was necessary. Palpatine's story that the Jedi had attempted to take over depended greatly on the public perception that Palpatine was an old man viciously attacked and deformed by the Jedi attempting to seize power. But Palpatine's story and hold on power would be undermined if he revealed himself as a Sith Lord:
- He would not be viewed as a defenseless old man attacked by the Jedi.
- The Jedi attempt to arrest him would appear far less traitorous.
- Order 66 would not be viewed as an emergency order to save the Republic from a takeover by the Jedi, but as an opportunistic order given on Palpatine's part to exterminate his ideological enemies.
Needless to say, Palpatine publicly revealing that he was a Sith would severely weaken his hold on power and the legitimacy of the Empire. The public perception of the Jedi Order would probably improve as well. Furthermore, Palpatine was always much more effective as a political ruler than an overt Force-user. He did kill a few Jedi in personal combat during the Clone Wars, but politically he engineered the destruction of the entire Jedi Order.
The canon novel Tarkin contains an interesting excerpt regarding the public knowledge about the Jedi attempt to arrest Palpatine and his identity as a Sith -- namely, that the public did not really know anything. Even Grand Moff Tarkin did not know exactly what happened when the Jedi attempted to arrest Palpatine, nor that Palpatine and Vader were Sith (he only suspected it):
There were many stories about what had occurred that day in the chancellor’s office. The official explanation was that members of the Jedi Order had turned up to arrest Supreme Chancellor Palpatine, and a ferocious duel had ensued. The matter of precisely how the Jedi had been killed or the Emperor’s face deformed had never been settled to everyone’s satisfaction, and so Tarkin had his private thoughts about the Emperor, as well. That he and Vader were kindred spirits suggested that both of them might be Sith.