Why did Rex call Palpatine Lord Sidious?
How Rex Knew to Call Palpatine Sidious During Order 66 - YouTube
The clones all say "yes, my lord" in Revenge of the Sith, which means they obviously knew to address him as Lord Sidious under the chip's influence and chose simply to say it in a different way.
When their efforts failed, Palpatine used the incident to frame the Jedi Order for treason and, as such, directed the clone army to execute their Jedi commanding officers in accordance with Order 66.
Palpatine was not given a first name in any canonical or "Star Wars Legends" sources until 2014, when the character's first name—Sheev—was revealed in the novel Tarkin, written by James Luceno.
Rex tries to resist his programming. He manages to tell Ahsoka to find Fives before he opens fire. Fives was a clone that discovered the truth about the inhibitor chips placed in the brains of the clones, how they could be used to turn the clones against the Jedi, and the first hints of Palpatine's true plans.
In 19 BBY, following Tyranus's demise, Palpatine revealed his identity as Darth Sidious to the Jedi Knight Anakin Skywalker, telling that the dark side teachings that Plagueis had pursued could help Skywalker to save his wife, whom Skywalker had foreseen dying untimely.
In any normal situation, they might be expected to be loyal to their generals; but as Juan pointed out above, these guys were bred for obedience. So they would obey their commander-in-chief - Palpatine - over any orders given by the Jedi.
Although Order 66 greatly depleted the Jedi Order's ranks, with an estimated less than 100 Jedi surviving it, it was only the beginning of the Great Jedi Purge, which stretched on for years and claimed the lives of many of the survivors of the initial onslaught.
In the 2005 film Star Wars Episode III: Revenge of the Sith, the villain Darth Sidious says, “Commander Cody, the time has come. Execute Order Sixty-Six.” This order makes clone troopers turn against Sidious' enemies, the Jedi knights, and kill them, setting off what's known as the Great Jedi Purge.
In the canon comic Darth Vader No. 25, it is revealed that Palpatine somehow used the Force to manipulate midichlorions to impregnate Shmi Skywalker.
Why can't the Jedi sense Palpatine?
How Come Yoda Couldn't Sense Palpatine? Yoda couldn't sense Palpatine because of the Jedi's own misteachings under his watch. He regretfully stated following the rise of the Empire that he and other Jedi Masters taught Younglings to stay away from the dark side.
Mas Amedda was the Vice Chair of the Galactic Senate during Chancellor Valorum's term, a position he continued to hold as Chancellor Palpatine transformed the Republic into the Galactic Empire.

Sidious himself felt that he and his peers had outgrown the use of lightsabers, and only continued carrying them to mock the Jedi. He ultimately viewed his own lightsabers as little more than an affectation, and rarely wielded them in combat.
Not so fast, young padawan. News broke over the weekend that a novelization of The Rise of Skywalker confirmed Emperor Sheev Palpatine was actually a clone in Episode IX, clearing up a major mystery from the actual movie.
Snoke Was a Strand-Cast Created by Palpatine
Emperor Palpatine created Snoke to be his proxy through which he could regain his power. Although Snoke was bio-engineered in a lab on Exegol, he was a strand-cast, not a clone.
Supreme Chancellor Sheev Palpatine is the ultimate evil in the galaxy of Star Wars, but one thing that gets lost in all of his cackling laughter is the fact that Palps is really freaking smooth.