During the Naboo blockade, the Jedi were faced with a serious question. The Sith, whom they should have destroyed a thousand years ago, suddenly appeared before the Jedi. The basis for this was the use of a red lightsaber. Yoda and Mace whisper to each other in front of Palpatine at Qui-Gon's funeral.
"Sith work in partnership, master and apprentice, no more, no less. No more, no less."
Lord Sidious pays the price of being made aware of the Sith's presence to the Jedi in exchange for his success in electing the Senate President. Upon arriving on Naboo, the Jedi Council retrieved and examined Maul's body and the Sith lightsaber. Of course, they do not know the name Darth Maul. However, it turns out that Darth Maul was alive in The Clone Wars season 3. This means that the Jedi had only recovered the lower half of his body on Naboo. In other words, Lord Maul was wandering around the Outer Rim with only his upper body, holding a lightsaber. (Incidentally, the Sith Inflator would be used by Sidious.)
Sabajio Press, who later became Dooku's apprentice, encounters Maul with the help of Mother Talzin after he is betrayed by Dooku. Meanwhile, when the Jedi notice Sabajio Press's presence, they mistakenly believe that he is the Sith killed by Obi Wan on Naboo. He knew Darth Maul's name and that his homeland was Dasmoor. (Some believe his homeland was Iridonia.)
Obi-Wan's investigation revealed that Savage was an acolyte of a Night Sister named Night Brother. However, there was no evidence of a master who had given Maul a dozen titles.
Obi-Wan reunites with Maul, who swears revenge, but the matter is not settled.
The retreating Maul and Savage join forces with the Deathwatch on the neutral planet of Mandalore to expand their power (the Shadow Collective). When Lord Sidious hears of this as Palpatine from the Jedi, he becomes impatient. He is surprised by the presence of his former apprentice, who is supposed to be dead, and warns him that he will be a hindrance to his plans. Neutral planets are inherently troublesome to the project, and above all, Maul knows who Lord Sidious is!
So Lord Sidious personally goes to Mandalore to take out Maul and Savage, who have seized power. Maul is kept alive. Maul is kept alive in order to find out if someone has revealed his identity to him. Thus, Lord Maul realizes that it is Lord Sidious who really owes him his loyalty. But Sidious no longer sees Maul as a Sith. But Sidious no longer sees Maul as a Sith, for he has a new apprentice, Vader.
So he arranged for Maul to become the head of the Crimson Dawn criminal organization. Sidious wanted to manipulate Maul to control Crimson Dawn from the shadows for the benefit of the Empire. As he wanted, Maul unites Crimson Dawn. He allowed the Sith doctrine to be used within the criminal organization.
Maul is unaware of the fact that Sidious's mentor was real. Sidious was wary of a face-to-face encounter between Playgus and Maul. Playgus could easily use Maul to betray Sidious because it was easily doable.
Sidious's training was grueling, but it was mostly done by droids. They are trained as Sith to specialize in assassinations, combat training, intelligence gathering operations, etc., and do not teach Sith plans. Thus, Maul, knowing that he was Sidious-Palpatine, did not become so troublesome as to interfere with the Sith plans. This is at the direction of Playgus.