One such moment occurred during episode 3 of the
Kenobi and Vader meet up once again in the series finale. This time, however, Obi-Wan is the one who overpowers his old disciple. He returns to Tatooine fully convinced that the man he once knew as Anakin has disappeared beneath the mask of Darth Vader.
Obi-Wan left Anakin for dead after their duel on Mustafar, but when they met again on the Death Star 19 years later the aging Jedi master knew who Darth Vader was under the helmet.
In Revenge of the Sith, at 01:37:38, Obi-Wan watches a security recording of Emperor Palpatine talking to Anakin and referring to him as “Lord Vader”. He KNOWS “Vader” is Anakin, and I seriously doubt that news of Vader's conquests across the galaxy failed to reach Obi-Wan, even if he was in exile.
Ten years after they clashed on Mustafar, Kenobi met again his old-friend-now-turned-bitter-enemy Anakin Skywalker, who completed his transformation into Darth Vader. The Sith Lord sought revenge for what happened when Kenobi mutilated him in Revenge of the Sith.
Only a Master of Evil
Up until now, the only meeting we've seen between Kenobi and Darth Vader was their final encounter. 1977's A New Hope saw the two aging warriors duel with lightsabers on the Death Star. "I've been waiting for you, Obi-Wan," Vader greeted Kenobi then. "We meet again at last.
Darth Vader hates Obi-Wan, not because he blames him for his fall to the Dark Side, but because he turned Padmé against him and destroyed his body.
Master Yoda knew that Darth Vader was once Anakin Skywalker- the boy he sensed too much fear in to train way back in Star Wars: The Phantom Menace.
If you are asking about Vader post-Mustafar, then no, she doesn't. Padmé doesn't seem to know Obi-wan cut off his limbs and left him to burn alive, Obi-wan didn't believe Anakin to be alive and Anakin's surgeries were still happening as Padmé died so there was no way for her to know.
Despite seeing Vader as an idol, Kylo conveniently ignored his grandfather's redemption. He was well aware of what happened, and it's likely Luke himself who told Ben about the events of Star Wars: Return of the Jedi.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
This might seem unexpected but it's worth noting that there are a couple of things that factor into Obi-Wan's inability to effectively stand his ground. Firstly, he hasn't fought in years. In order to hide from the Empire, he needed to keep a low profile. This means that he's not in his best fighting form.
The reasoning comes from, not only his fears that he isn't strong enough to defeat Vader after 10 years in hiding but the fact that facing Vader means Obi-Wan will have to face up to his greatest failure.
Why does Obi-Wan Kenobi age like that? Because he's not real, and is a fictional character played by different people. You see, Obi-Wan Kenobi is played by Alec Guinness in the original trilogy. Guinness was 62 when he filmed A New Hope, and he died in 2000.
Obi-Wan Kenobi and Anakin Skywalker/Darth Vader have fought four times on-screen, but the Star Wars canon suggests there is one unseen battle between former master and apprentice.
Leia doesn't get to reunite with Obi-Wan, and instead, just before escaping with Han and Luke, she sees his murder. Of course, Leia doesn't know Darth Vader is her father yet, either in A New Hope and certainly not in Obi-Wan Kenobi. But for the most part, the narrative focus of A New Hope is on Luke.
Anakin does not have even the slightest bit of remorse. By the end, he feels nothing but anger. Although he feels regret for killing Padme, he still helps the evil Emperor. The film ends with Anakins standing side by side with the man on whose behalf he has committed all his crimes.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
Yoda. Yoda's knowledge of Luke Skywalker's true parentage was also confirmed in Return of the Jedi. As with Obi-Wan, Yoda believed that Anakin's fall to the dark side made him unsalvageable, with the Darth Vader persona being his only identity following his ascension to Sith Lordship.
Anakin Skywalker is the son of Shmi Skywalker, born without a father through the Force. He is the secret husband of Padmé Amidala, the father of Luke Skywalker and Leia Organa, the father-in-law of Han Solo, and the maternal grandfather of Ben Solo.
Arguably, most Star Wars plot points revolve around characters simply not knowing something, very often about their family history. But, on top of all of that, the biggest reason Obi-Wan doesn't know Anakin is alive is that the last time he saw Anakin Skywalker in Revenge of the Sith, Ben literally left him for dead.
During the iconic opening moments of Star Wars: A New Hope, Darth Vader has a tense confrontation with Princess Leia, an adversary who, unknown to him, is actually his daughter. Despite participating in Leia's interrogation, the Sith Lord doesn't uncover his familial connection with the rebellious royal.
He slays Sidious and returns to Obi-Wan, begging for atonement by execution, only to be met with true forgiveness instead. But just as this fantasy Obi-Wan refuses to strike his former friend down, Vader refuses to turn his back on the dark.
The added risk Darth Vader takes in allowing children to live in a situation where he could have killed them proves that he regrets killing Younglings and will avoid harming any more children for the rest of his days, though intense intimidation is a dark strategy to avoid repeating his Youngling massacre.