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.
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.
The lack of recognition could have come from an old man simply not remembering the passing droids of his youth. Lastly, Owen didn't seem the sentimental type to form any emotional attachments to droids. Being a practical man, he viewed them as tools to be used and replaced when they no longer functioned.
Finding Threepio's brain devoid of such detail, Cad targeted R2-D2 next, where he found what he was looking for. 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.
Why Doesn't Obi-Wan Remember R2-D2 in A New Hope? - Star Wars Explained
Did R2-D2 know Darth Vader was Anakin?
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.
They aren't abbreviations — they're model and serial numbers. R2 is a second generation R-series astromech, serial number D2. * And C-3PO is a C-series protocol droid with the serial number 3PO.
What happened to C-3PO and R2-D2 after Revenge of the Sith?
Shortly after the Clone Wars, C-3PO's memory was erased, though R2-D2's memory was not. C-3PO and R2-D2 were assigned to the Alderaan cruiser Tantive IV, where they served senator Bail Organa for nineteen years, assisting in his fledgling resistance movement against the Galactic Empire.
Since Bail Organa had C-3PO's memory wiped previously in order to prevent him from spilling the secret of Leia's parentage, it could be that this was a semi-regular occurrence for the droid given he couldn't be trusted to keep quiet about things.
Artoo not only knew this info in A New Hope, he also knew about this way back in Revenge of the Sith when Bail, Obi-Wan, and Yoda were on the Tantive IV, going back to Coruscant. C-3 had his memory wiped, so as far as we know, he can't remember about Anakin turning.
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.
Instead, the diminutive droid appears to have kept his own counsel, perhaps wary of interfering too much in Luke's personal journey. C-3PO lost those memories, but he remained with Han and Leia's family after Return of the Jedi, so can reasonably be assumed to have learned the truth by eavesdropping.
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.
Anakin Skywalker's birth mystery is solved - his mother, Shmi Skywalker, reveals that there was no father and she can't explain what happened. Qui-Gon Jinn believed that the Force itself created Anakin in Shmi's womb, making him the Chosen One who would bring balance to the Force.
R2-D2 (/ˌɑːr. tuːˈdiːtuː/) or Artoo-Detoo is a fictional robot character in the Star Wars franchise created by George Lucas. He has appeared in ten of the eleven theatrical Star Wars films to date, including every movie in the original trilogy, prequel trilogy, and sequel trilogy.
He is programmed to prioritize the safety of his companions, which can sometimes lead to his overprotective behavior. C-3PO's worrying nature is also a result of his experiences throughout the Star Wars saga. He has been through many dangerous situations and has witnessed the destruction and chaos caused by the Empire.
He didn't recognize him because again, they all look the same & it was decades until he saw him again. There was no reason to believe he or R2 even existed anymore.
secondly, in Legends, R2 was given programming that actually restricted him. from sharing any information with Luke or Leia. about their parents or relation to one another. this was all part of the plan. to conceal this information from the twins.
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.
R2 was later able to restore his companion during the Battle of Geonosis. 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.
Unfortunately, Rex and Vader never meet again though. Why didn't Palpatine feel afraid of showing his evil actions, behaviors and ways to Anakin and the Jedi anymore?
