Obi-Wan Was Pretending He Didn't Know R2-D2 The base assumption of why Obi-Wan doesn't remember R2-D2 -- in light of the prequels -- is that Obi-Wan is feigning ignorance in A New Hope to downplay the importance of the droid's arrival.
Obi-Wan never technically owned R2-D2 or any droid in the prequels. R2 belonged to Padmé Amidala before she gifted him to Anakin Skywalker, and after the war, both R2 and C-3PO became the property of Bail Organa. Obi-Wan knew him, but never owned him.
According to one article (via Looper), Obi-Wan recognized R2-D2 but simply decided not to tell Luke. When Luke asked Obi-Wan about his father, Obi-Wan stated that Darth Vader killed Anakin, which later turned out to be a symbolic description for Anakin becoming Darth Vader.
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.
Conclusion. Although Darth Vader certainly suffers from repressed memories and trauma, it's clear that he still remembers R2-D2 and C-3PO.
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.
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.
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.
According to the comics (which are canon), yes. See this image below: This came from Cloud City (Bespin). Remember that this is the first (and only) time Vader saw C3PO after RoTS.
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.
It's because of his mastery of sorsue (sorry for my bad spelling.) Well if you want the ACTUAL reason it because in the original 3 films the Green Light Sabre didn't exist until after Obi Wans death.
“It's good to fly with you again, my old friend,” the old man said, so softly Han wasn't sure he had heard him right. C-3P0 didn't; his memory was wiped at the end of Revenge of the Sith to prevent him from spilling the beans.
After Cad Bane had kidnapped and ransacked the memory of C-3PO and R2-D2 for information on the Senate Building's layout, he only had the incident wiped from their memories to avoid having any suspicion falling on him.
C3PO's restraining bolt put him in safe-mode and prevented him from full memory access. As an aside, R2 also had a restraining bolt, which prevented him from full message playback of Leia's "secret mission" message.
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.
While, it may be true Chewbacca met Yoda and Ahsoka, there is no indication that he met Anakin. Even if Chewbacca has met Anakin, Chewbacca would have assume Anakin was one of those Jedi killed in Order 66. How would he know who Luke's father was? There is no evidence they ever met, never mind actually knew each other.
Vader relies on the complex life support system of his suit to survive and it happens to be very vulnerable to electrical discharges. So, if Vader ever had unleashed Force lightning, there's a good chance it would've caused his suit to short circuit, thus, killing him.
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.
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.
R2-D2, the indomitable droid and mainstay of the Star Wars series, may be responsible for one more incredible feat: saving Grogu.
C-3PO accidentally became part of the Battle of Geonosis when his head was affixed on top of a battle droid's body after a mishap in the Geonosian droid factory. R2-D2 and C-3PO witnessed the secret wedding between Anakin Skywalker and Padmé Amidala on Naboo.
In "The Empire Strikes Back," Darth Vader stops Boba Fett from shooting Chewbacca because he has plans for the Wookiee.
Unlike the droids (i.e., C-3PO and R2-D2) Obi Wan's memory wasn't wiped.