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.
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.
Shortly after the Galactic Empire was formed, Bail Organa, in order to protect Princess Leia, had C-3PO's memory wiped clean in order for the droid to not spill any confidential information, especially information related to Leia's true lineage, which would make her a target of the Emperor.
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.
Why Doesn't Obi-Wan Remember R2-D2 in A New Hope? - Star Wars Explained
How does C-3PO not remember Princess Leia?
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.
Because Bail Organa ordered C3PO's memory wiped at the end of the Revenge of the Sith. This was to protect the twins identity because he knew that C3PO had a tendency to run off at the mouth!
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.
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, ...
At the end of Star Wars: Episode III - Revenge of the Sith, C-3PO's memory was wiped, allowing him a fresh start by the time A New Hope begins, but R2-D2's memories remained intact, which is why many fans wonder why he didn't tell Luke the truth about his family history, but he might have not done that because he didn' ...
in the Dark Horse comic series star Wars Tales, which is now part of legends, it's revealed that Darth Vader did recognize C. 3PO on Cloud City. when 3PO was shot by Stormtroopers, his parts were brought before Vader. because the Imperials thought he could hold valuable.
She senses Anakin when she reaches out to the pilot — and Vader realizes that Ahsoka, his former Padawan, lives on. In Season 2, Episode 18, “Shroud of Darkness,” Ahsoka's guilt manifests as a vision of Anakin, who's angry with her for leaving him all those years ago.
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.
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.
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 Star Wars: The Force Awakens, set approximately 30 years after Return of the Jedi, R2-D2 is revealed to be kept in storage at the Resistance base on the planet D'Qar, having put himself in a low-power mode after Luke Skywalker's disappearance.
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.
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.
However, while Yoda acts as though he had never met R2-D2 before, the Star Wars prequel trilogy, released decades later, revealed that Yoda was already well acquainted with the famous astromech droid.
While in the Ewok village, Luke revealed his true lineage to Leia. She was shocked to discover they were brother and sister, though deep down, she always knew this to be true.
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.
It is believed that Leia didn't have actual memories of their mother, but visions of her through the Force, which she believed to be memories. As Leia was born after Luke, if he didn't remember her, she wouldn't either.
