Obi-wan responds to starwars.wikia.com/wiki/Luke_Skywalker saying R2 belongs to him with, “I don't seem to remember ever owning a droid,” which is technically true, because Obi-Wan never did “own” R2 or C-3PO. Obi-Wan then makes a comment that suggests he's more than aware of R2's impressive capabilities.
Summary. Obi-Wan's seeming inability to remember R2-D2 in "A New Hope" was a deliberate choice to downplay the droid's arrival and avoid revealing too much too soon.
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.
In George Lucas's head, it's very possible Obi-Wan had actually never met R2 prior to their joint presence on Tatooine. Only later, as other movies were released, did such circumstances change. However, there are Star Wars fan theories suggesting Obi-Wan pretended not to know R2 on purpose.
The real reason why Obi-Wan Kenobi, the Lars family, or Darth Vader didn't act in the original Star Wars trilogy as though they knew C-3PO or R2-D2 previously is that the prequel trilogy, in which they first meet the two droids, had not been written yet.
Why Doesn't Obi-Wan Remember R2-D2 in A New Hope? - Star Wars Explained
Did R2-D2 know Anakin was Darth Vader?
Darth Vader's true identity as Anakin Skywalker was a highly guarded secret, known only to a select few individuals including Palpatine, Obi-Wan Kenobi, Luke, Han, Leia, R2-D2, C-3PO, Master Yoda, Bail Organa, Ahsoka Tano, Darth Maul, Grand Moff Tarkin, Grand Admiral Thrawn, Jocasta Nu, Ferren Barr, Verla, Reva, ...
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.
In The Phantom Menace, set 32 years before A New Hope, R2-D2 is portrayed as belonging to the Naboo defense forces, one of three astromech droids deployed for repair duty onboard Queen Padmé Amidala's (Natalie Portman) starship as it attempts to get past the Trade Federation blockade.
The sequence calls back to a similar scene in Revenge of the Sith, when Bail Organa orders Threepio's memory be erased to prevent him from sharing information about Anakin Skywalker's fall to the dark side.
Bail's final line of the film and instruction to the Captain, says “…have the Protocol droid's mind wiped.” Because Bail Organa had them wipe his memory at the end of Revenge Of The Sith and he never came back to Tatooine until A New Hope.
Because as far as he knows it's just a generic protocol droid. There are millions of them all over the galaxy. He has no reason to think this droid is the same one he was briefly acquainted with many years ago.
C-3PO's memories were (against his own wishes) wiped again on Kijimi when the droidsmith Babu Frik bypassed C-3PO's programming restrictions to allow the droid to translate the Sith writings on a Sith dagger. C-3PO's photoreceptors turned red while he translated the forbidden inscriptions.
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.
In canon, Vader found out because Luke told Boba Fett that he was “Luke Skywalker.” This was explained in the canon comic Star Wars (2015) 5. Vader only sensed Leia was Luke's sister because Luke was thinking about her on the Death Star II. When Vader tortu…
After decades of missions with R2-D2, Luke Skywalker was reasonably fluent in droidspeak. The most common way for binary droids to communicate with organics was by writing, conveyed via another computer system. This is how astromech droid copilots would speak with the pilot of a starfighter.
When Luke Skywalker arrived on Dagobah in 3 ABY, the King of the Dragonsnakes swallowed his astromech droid R2-D2, but then spit the droid back out due to its being indigestible.
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.
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.
