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.
R2-D2 did. According to the canon Star Wars book The Princess, the Scoundrel, and the Farm Boy: The R2 unit moved to Ben's side as if it were his faithful pet — an image that was further reinforced by the old man's stroking a hand over its domed head.
You'll remember that, in the conclusion of Revenge of the Sith, C-3PO's memory is wiped, so he loses his knowledge of the past. R2's isn't stated to be erased, so he presumably maintains his memories; why does he never tell Luke about Anakin?
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.
Meanwhile, R2-D2's cameo in Obi-Wan Kenobi comes a bit later on at the 38:45 mark of the episode. He's briefly shown on the right side of the screen as Bail and Breha Organa talk about Leia. The appearances of R2-D2 and C-3PO in Obi-Wan Kenobi work perfectly within the established Star Wars canon.
Yoda recognized R2-D2 during The Empire Strikes Back.
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.
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.
Star Wars Characters That Can Understand Droids
While all droids understand Binary, only a handful of living creatures can. Canon characters, such as Anakin Skywalker, whose relationship with R2-D2 is one of the best in the whole series, Rey, Poe Dameron, Hera Snydulla and Kazuda Xiono are fluent in the droid language.
Yes, he did. In the comic Thank the Maker, Darth Vader comes into possession briefly of 3PO's disassembled head while on Cloud City.
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.
Obviously, C-3PO does not recognize Vader because his memory was wiped at the end of Revenge of the Sith.
The two droids were dumped back on the streets, their memories wiped of the incident. Unlike R2-D2, Threepio's mind is wiped of all memories after the birth of Luke and Leia.
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.
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
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.
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.
C-3P0's memory was wiped at the end of Episode III so if he wasn't told he had no idea that his maker was the future Darth Vader. R2-D2 remembers it all and if I had to guess he is quiet sad about Anakin's turn to the dark side.
Unlike C-3PO, little about R2-D2's previous life is known. In old Star Wars canon, he was purchased by the Royal Engineers of Naboo, who made after-market additions to the droid before shipping him out into space.
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.
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.
Does Darth Vader remember being Anakin? Yes. Yes, he remembers his name but feels it has no meaning to him anymore.
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.
R2 doesn't know it. It's as simple as that. He isn't present on Mustafar (he flies with Anakin but is ordered to stay at the ship. He isn't present while the slaughtering of the seperatists or the fight of Anakin/Obi-Wan.), differently to Obi-Wan and C-3PO.
By claiming he's never owned a droid, he applies the same tactic as he did with his embellishment about Anakin. 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.