star wars - What did the general public know about Darth Vader?

When Darth Vader first becomes Palpatine's apprentice, very few know of his existence and connection to the Emperor: the members of the Trade Federation (whom he dispatches) and Yoda, Kenobi, Organa, and their associates are all that seem to know at the end of Episode III.

Ultimately, the Resistance would know about him as they would be fighting him, and Organa could have been able to inform them about his identity and the fact that he is a Force user. The military of the Empire would know of his existence, but even high-ranking members likely wouldn't know his past or identity. However, they would know about the fact that he is a Force user due to his tendency to use his "sorcerer's ways" to choke people.

So, how much would the general public have known about Vader? Would they have known him as just another military leader, or would they have known he was Palpatine's right-hand man? Would they have known about his ability to use the Force, and therefore the possibility that he was a Sith?

Answer

Restricting ourselves to canon, the novel Tarkin provides a nice list of rumors surrounding Vader:

It was that genuflecting obedience, the steadfast devotion to execute whatever task the Emperor assigned, that had given rise to so many rumors about Vader: that he was a counterpart to the Confederacy’s General Grievous the Emperor had been holding in reserve; that he was an augmented human or near-human who had been trained or had trained himself in the ancient dark arts of the Sith; that he was nothing more than a monster fashioned in some clandestine laboratory. Many believed that the Emperor’s willingness to grant so much authority to such a being heralded the shape of things to come, for it was beyond dispute that Vader was the Empire’s first terror weapon.

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As you suspected, not many members of the Imperial military knew of Vader's past. The novel Tarkin also hints at this, as even the high-ranking Moff Tarkin did not know of Vader's past and could only harbor suspicions based on his past experience with Anakin:

Very early on in their partnership—soon after both had been introduced to the secret mobile battle station—Tarkin grew convinced that Vader knew him much better than he let on, and that behind the bulging lenses of his face mask, whatever remained of Vader’s human eyes regarded him with clear recognition. More than anything else it was those initial feelings that had provided Tarkin with his first suspicion as to Vader’s identity. Later, observing the rapport the Dark Lord shared with the stormtroopers who supported him, and the technique he displayed in wielding his crimson lightsaber, Tarkin grew more and more convinced that his suspicions were right. Vader might very well be Jedi Knight Anakin Skywalker, whom Tarkin had fought beside during the Clone Wars, and for whom he had developed a grudging appreciation.

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