In the final film, Revenge of the Sith, the two droid companions continue to work closely alongside Obi-Wan, Anakin, Padme, and others. Throughout the years,
Obi-Wan Kenobi has no idea who C-3PO is when they meet in “Star Wars: A New Hope” even though the prequel trilogy later told us that the two certainly knew each other.
Obi-Wan did in fact remember R2D2 after the little smirk he gave after seeing him in ANH when he rescued Luke from the sand people. C3PO had his memory erased so he doesn't remember at all.
Obi Wan and R2 interact frequently in the prequels - given the timeline, it seems odd that Obi Wan would have absolutely no recollection of R2. Unlike the droids (i.e., C-3PO and R2-D2) Obi Wan's memory wasn't wiped.
Since Obi-Wan and Anakin often fought together, Obi-Wan was friends with R2-D2 as well. This means that although R2-D2 might not have immediately recognized Obi-Wan on Tatooine due to his age, Obi-Wan should have recognized the droid.
Perhaps, the old creature simply forgot. Late in the film, Darth Vader does not recognize C-3PO who is in Cloud City with Han Solo, Chewbacca, and Leia. Although C-3PO is not completely assembled in the scene, he is definitely visible to Vader.
Revenge of the Sith
After Anakin falls to the dark side of the Force and becomes Darth Vader, he takes R2-D2 with him when he goes to assassinate the Separatist council, but tells him to stay with the ship.
Such cycles of fate no longer surprised the nine-hundred-year-old Jedi. So there you have it. Yoda and R2D2 knew each other and the galaxy is even a smaller world than we think.
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.
When R2D2 was missing in action, Anakin went to great lengths to rescue him, even distrusting his replacement droid, which turned up to be a mole planted by General Grievous. R2 was on Mustafar when Anakin became Vader. That, perhaps, explains that he doesn't try to reacquire him.
He does. In the comic Star Wars Tales #6, we see an interaction between Vader and C-3PO. In the comic, Boba Fett brings Vader C-3PO's remains. Vader instantly recognizes C-3PO, and is reminded of his childhood.
C-3P0 didn't; his memory was wiped at the end of Revenge of the Sith to prevent him from spilling the beans. C3PO, no. His memory was wiped at the end of Revenge of the Sith. A blabbermouth like him can't be trusted with sensitive information.
As we all know well, in A New Hope, Obi-Wan went to Mos Eisley to meet with Chewbacca and Han, in order to get off Tatooine to get R2-D2 to the Rebellion. By the end of Revenge of the Sith, Obi-Wan and Chewie didn't meet, at least that we have seen.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Vader agreed to help the handmaiden, silently recalling the time he spent with Padmé in the process. In this moment, he was once again Anakin Skywalker, a young man in love who simply wanted to change the world for the better.
Does Darth Vader remember being Anakin? Yes. Yes, he remembers his name but feels it has no meaning to him anymore.
After the battle, R2-D2 and C-3PO were the sole witnesses to the marriage of Anakin Skywalker and Padmé Amidala in Lake Country. After this Padmé gave ownership of R2 to Anakin while she kept 3PO.
Both R2D2 and C3PO both know that Darth Vader and Anakin are one and the same. 3PO's memory was erased back in Star Wars Episode III: Revenge of the Sith but was restored by R2 back in Star Wars Episode IV: The Rise of Skywalker. As such, they both remember everything that happened.
Remember that this is the first (and only) time Vader saw C3PO after RoTS. Threepio was getting pushed into an escape pod by R2D2 by the time Vader entered their ship in ANH. Though he was chased throughout the original series, this was the only time Vader actually saw Threepio, again.
He hasn't owned a droid because R2-D2 is his friend. No one can "own" him, and to claim to have done so disrespects the countless ways the little astromech has saved the galaxy. If the theory applies, then Obi-Wan cleverly makes note of that while simultaneously hiding his past companionship with R2-D2.
R2-D2, the indomitable droid and mainstay of the Star Wars series, may be responsible for one more incredible feat: saving Grogu.
Darth Vader can not use force lighting, because of his severed arms. Robotic hands can't summon the force lighting. However Darth Vader can still use other forms of the force, such as force choke.
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. "Sister," the Emperor taunted. "So... you have a twin sister.
Leia Organa-Skywalker
Leia Amidala Skywalker (portrayed by Carrie Fisher) is the wife of Han Solo, the mother of Ben Solo, the younger twin sister of Luke Skywalker, the daughter of Anakin Skywalker and Padmé Amidala, and the granddaughter of Shmi Skywalker, raised by Bail and Breha Organa of Alderaan.