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.
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.
What's going on: Anthony Daniels, who plays the C-3PO role in all of the nine Skywalker saga films, recently told HuffPost that he wasn't sure why Obi-Wan Kenobi didn't know C-3PO. He said it's possible Obi-Wan knew too many droids.
Meanwhile, R2-D2's cameo in Obi-Wan Kenobi comes a bit later on at the 38:45 mark of the episode. He's briefly shown on the right side of the screen as Bail and Breha Organa talk about Leia. The appearances of R2-D2 and C-3PO in Obi-Wan Kenobi work perfectly within the established Star Wars canon.
Why Doesn't Obi-Wan Remember R2-D2 in A New Hope? - Star Wars Explained
Did R2-D2 know Vader was Luke's father?
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.
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.
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.
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.
Either way, while Vader can use most other Force abilities, Force Lightning needs to be channeled, and Vader's limbs are explicitly not connected to the Force. The Star Wars: Episode III - Revenge of the Sith Visual Dictionary confirms Darth Vader cannot use Force Lightning, and even suggests this is the reason why.
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.
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.
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.
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.
In the years before the Clone Wars, R2-D2 served the Royal House of Naboo. He was aboard Queen Amidala's royal starship when she tried to run the Trade Federation's blockade. Artoo repaired the ship's damaged shields under heavy fire, allowing it to escape into hyperspace.
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.
Because he never owned a droid. R2-D2 was owned by Padme and later Anakin, and after that Bail Organa. R4-P17 was assigned to him to assist, not given to him to own. So he really never owned one.
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.
Three months after the Battle of Endor, Skywalker used the lightsaber during a mission to an Imperial research base on the planet Vetine in order to retrieve the last remaining fragment of a Force-sensitive tree. Skywalker gave his lightsaber to R2-D2 for hiding as they entered the Imperial base.
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.
