Darth Vader learns the name in the opening scene while torturing a Rebel, though in this case, he only learns Luke's surname of Skywalker, making the Sith Lord's discovery in the classic Marvel series Luke's first name.
Luke's original surname was "Starkiller", and it remained in the script until a few months into filming. It was dropped due to what Lucas called "unpleasant connotations" with Charles Manson, who became a "star killer" in 1969 when he murdered the well-known actress Sharon Tate.
Darth Vader learns the name in the opening scene while torturing a Rebel, though in this case, he only learns Luke's surname of Skywalker, making the Sith Lord's discovery in the classic Marvel series Luke's first name.
The two recognize Luke's similarities to Anakin and try to prevent him from sharing his father's fate, but they let him remain Luke Skywalker instead of having him go by Luke Lars out of respect for his grandmother, Shmi Skywalker.
R2-D2 was present when Padmé gave birth to Leia and Luke, so he knew Luke was Anakin's son – but what he didn't know was that Anakin became Darth Vader. In addition to that, Anakin's fall was surely a painful event in R2-D2's life, one that he definitely wouldn't like to remember or even talk about.
How Darth Vader Found Out Luke Skywalker Was His Son (Canon) - Star Wars Explained
Did Vader ever know Leia was his daughter?
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence.
It was believed that Grogu would eventually become a victim of Kylo Ren's destruction of Luke's Jedi Order. However, The Book of Boba Fett revealed that Grogu chose to follow the Way of the Mandalorian rather than become a Jedi, sparing him from Kylo Ren's wrath.
Within Vader still resides a part of his former self, Anakin Skywalker, and it could be argued that this is why he can sense Luke while the Emperor cannot.
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.
Darth Vader acts like he doesn't even know C-3PO or R2D2. They were with him since he was a child. He did everything he could to forget his past. Also, his plating had been replaced many times, and protocol droids all look very similar.
Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection. Vader's denial of Anakin Skywalker's legacy and his fear of getting hurt again prevented him from realizing the truth about his children until later in the original trilogy.
The question being answered is: “Do R2D2 and C3PO know that Darth Vader is Anakin?” C-3PO? Definitely not. As many other have pointed out, C-3PO had his memory wiped at the end of Episode III, so it is almost certain that he does not know.
Luke became famous after destroying the Death Star, putting him right in the crosshairs of the Empire. As The Empire Strikes Back picks up, Vader is obsessively searching for Luke, due to their familial connection.
Maybe R2-D2 didn't know Darth Vader was Luke's father because he didn't see Palpatine christening him Vader, or maybe he believed Anakin was dead because even Obi-Wan didn't know Anakin was alive.
Owen felt that Obi-Wan was personally responsible for the deaths of Shmi and Anakin and, that the Jedi Master's actions had ripped his family apart. Despite his dislike of the Jedi and Kenobi in particular, Owen did have honor, refusing to turn Kenobi in when several Sith Inquisitors came looking for him.
Owen and Beru decided to have a child, but problems of infertility precluded them to have one, leading them to consider seeing one of the fertility droids at Mos Eisley.
Though it sounds like he thinks Anakin is dead, he could also be viewing it as Obi-Wan does, where he believes Anakin died when Darth Vader was created. There's a hint that Owen knows Anakin was Darth Vader by the time of A New Hope.
