star wars - Did the 501st Legion know what Anakin had become when they attacked the Jedi Temple with him?

When the 501st Legion ("Vader's Fist") attacked the Jedi Temple as part of Operation: Knightfall, they were led by an unmasked Darth Vader:

Did the members of the 501st know, at that time, that Anakin had become a Sith Lord and was now Darth Vader?

It is tempting to say that the answer is obviously "yes", because why else would a Jedi attack the Jedi Temple? However, answers to related questions note that it was publicly believed that Anakin had died in the Jedi Temple defending Jedi children and, furthermore, even high-ranking members of the Imperial military -- such as Moff Tarkin -- did not know with certainty that Anakin was Vader. Obviously, the 501st knew that Anakin helped them attack -- not defend -- the Jedi Temple, and they probably knew he was very much alive at the end of the attack. Moreover, if the 501st knew Vader's true identity, then they must have kept that fact from high-ranking Imperial officers since those officers did not know Vader's true identity. It would be a truly impressive display of operational security if an entire legion of troops managed to hide Vader's identity from even Imperial officers. This is only plausible because the 501st is composed of highly trained and professional soldiers who also happen to be clones bred for obedience.

It is difficult to explain what happened if the answer is "no", too, though. In that case, the 501st was presumably told that all the Jedi were traitors but that Anakin had defected from the Jedi. Since Anakin had previously commanded the 501st in the Clone Wars, it made sense that he would lead them in the attack. But that still doesn't explain how the 501st were led to believe that Anakin died in the Jedi Temple -- he'd have to somehow duck out in the middle of the battle, fake his death, and then explain how not a single clone in the Temple found his corpse.

Is there a source which definitively answers whether the 501st knew Anakin was Darth Vader during the attack on the Jedi Temple? For example, a source which includes a quote of Anakin calling himself Vader in the Jedi Temple and in the presence of clones from the 501st would prove that the 501st knew his true identity; on the other hand, a source which includes a quote of a 501st clone referring to Vader as Anakin would indicate that the 501st did not know the two were the same man.

Canon answers are preferred, although Legends answers are acceptable if canon is silent on the issue.

Answer

In both canon and Legends, the 501st Legion/Clone Battalion is the clone unit attached personally to Jedi General Anakin Skywalker during the Clone Wars. It is the unit Anakin, now Darth Vader, led to the attack on the Jedi Temple. It is the unit that becomes Darth Vader's personal army during the Imperial era, and will become known as Vader's Fist.

The canon explanation is the only version with potential plot holes. Inhibitor chips overrode the clones' conscious control of themselves (Rex removed the chip, but he resigned from his post after Fives' death, so is probably transferred out and thus wasn't there to know the truth). I can't remember which source I saw this from, but I read somewhere between Dec to Feb that clone veterans after the war described the experience as their vision akin to being clouded with bloodlust. It's possible that the clones of the 501st themselves didn't know what happened, and so believed General Skywalker died defending the Temple, and they would hereafter be commanded by Lord Vader.

Like I said, I can't cite to support the above explanation, so this remains as a plot hole. If the above isn't true, then something has to be done about those clones who know. However, it remains that after the clones are retired in favour of birth-born Stormtroopers, Darth Vader's true identity is henceforth unknown to the birth-born stormtroopers of the 501st.

In Legends, the clones definitely know. The 501st Legion was specifically selected by Palpatine for additional training in secret. They served Palpatine's Sith agenda privately. When the time came for Order 66, the 501st was transferred back to Coruscant under the command of Darth Vader, who is the very General Skywalker whom they had served under for 3 years. It would be impossible not to recognise him.

Here's a clip of Operation: Knightfall in Battlefront II. If you consider the text on the loading screen and the in-game scripted speech to be canon (The Holocron system identifies all plot-related elements of licensed games to be EU/C-Canon), then the clones of the 501st are explicitly identifying Anakin as Lord Vader during the attack on the Jedi Temple.

In the above clip, we observe the clones of the 501st referring to General Skywalker as "the newly anointed Lord Vader". Clearly, the 501st (or at least the officer corps who would be in direct contact with Vader) knew a lot more than the rest of the galaxy.

After the Clone Wars concluded, the 501st Legion is placed under Darth Vader's personal command:

With the fall of Coruscant and the elimination of the traitorous Jedi, Palpatine's rise to power was complete. In recognition of our service and loyalty to the Emperor, the 501st were placed under the direct command of Lord Vader. Armed with deadly new weapons, blazing new ships, and shiny new armor, our presence let the galaxy know that the days of the Old Republic were well and truly over. We were establishing a new era, an era of order and peace.

What is important is that Darth Vader is outside of the normal chain of command. The 501st is fiercely loyal to none but Emperor Palpatine and Darth Vader - so much so that Palpatine trusted the 501st enough to keep them as purely Fett clones even though, after the Clone Rebellion of Kamino, he believed a purely Fett army in general is too vulnerable to subversion.

Put this all together, and the 501st answer to no Imperial officer but Darth Vader, and the Imperial officers can do nothing about it. They will also not do anything that will endanger their true loyalties - if the Emperor wants the galaxy to think Anakin Skywalker is dead, then they will make it so.