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.
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.
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.
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, ...
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.
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.
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.
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.
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.
According to Imperial Estimates in Star Wars Inside #87, only about 100 of the Jedi survived Order 66. Most were subsequently hunted down and killed in the years following the Great Jedi Purge.
Does KYLO Ren know Darth Vader is his grandfather?
Kylo Ren was always obsessed with his grandfather. He didn't learn he was the grandson of Darth Vader until he was a teenager, when a recording from Bail Organa - intended to be a private message for Leia - was shared with the entire galaxy.
At first, Ahsoka has no idea that Anakin Skywalker and Darth Vader are one and the same. She discovers the truth in Star Wars Rebels when she encounters the Sith Lord in a space battle. What she senses is so shocking to her that she passes out.
However, R2-D2's memory is not wiped; as a result, R2-D2 is the only surviving character at the end of the saga who knows the entire story of the Skywalker family. Both R2-D2 and C-3PO end up in the possession of Captain Raymus Antilles (Rohan Nichol) onboard the Tantive IV.
Since Obi-Wan and Anakin often fought together, Obi-Wan was friends with R2-D2 as well. This means that although R2-D2 might not have immediately recognized Obi-Wan on Tatooine due to his age, Obi-Wan should have recognized the droid.
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.
In the comic Star Wars Tales #6, we see an interaction between Vader and C-3PO. In the comic, Boba Fett brings Vader C-3PO's remains. Vader instantly recognizes C-3PO, and is reminded of his childhood.
Anakin never really had the chance to process his experiences and has to rely on short-term defence mechanisms to protect himself from the painful memories. This is all the more tragic because he is aware of this and yet finds himself unable to find comfort in somebody, not even in his wife.
