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.
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.
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. That explanation holds the most water for a number of reasons.
R2-D2 witnessed some of Anakin's best moments and knew him when he was an innocent boy on Tatooine; it might have been healing for Luke to hear these stories. Perhaps, like the stories about Padmé, they were simply too painful to share.
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.
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.
Absolutely. Growing up on Tatooine, Anakin Skywalker was already accustomed to grasping and understanding many different languages. Not to mention, he was a droid fanatic himself—being a great mechanic—and most likely knew the language of Artoo's “droid language” or picked up on it quite quickly.
By wiping his memory, it allowed the leeway necessary to bridge the logic gap created by the previous two prequel films. However, the same could not be said for R2-D2, who never had his memories erased.
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.
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.
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.
However, one theory argues that Obi-Wan did recognize R2-D2, but he chose to pretend not to in order to avoid telling Luke the full truth. This would explain certain signs of familiarity between the Jedi and the droid and fit Obi-Wan's pattern of subtly lying to Luke.
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.
The Invasion of Naboo. R2-D2 repairs the shield generator of Queen Amidala's Royal Starship. In 32 BBY, R2-D2 was in the possession of the Royal Engineers of Naboo, and was assigned aboard Queen Amidala's Royal Starship as a maintenance droid.
The name derives from when Lucas was making one of his earlier films, American Graffiti. Sound editor Walter Murch states that he is responsible for the utterance which sparked the name for the droid. Murch asked for Reel 2, Dialog Track 2, in the abbreviated form "R-2-D-2".
Together, Palpatine and Vader commanded the Empire's army of stormtroopers. Vader lacked any kind of formal rank and was simply regarded as a "lord" by stormtroopers or any other Imperial. Imperial stormtroopers rallied behind Darth Vader, who they seemed to basically worship as the hero of the Empire.
Luke hid his lightsaber inside R2-D2's dome during his mission to rescue Han Solo from Jabba the Hutt, and surrendered the weapon to Darth Vader as part of his effort to reawaken the spirit of Anakin Skywalker.
Programmed for etiquette and protocol, Threepio was built by a young Anakin Skywalker, and has been a constant companion to astromech R2-D2. Over the years, he was involved in some of the galaxy's most defining moments and thrilling battles.
In Padme, Anakin never returns. So R2 spends the next 20+ years believing his friend. perished on Mustafar. So throughout The Empire Strikes Back, every time Luke tells R2 to stay with the ship, R2 ignores him.
