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.
C3PO was clearly created from some sort of kit or existing prototype since every protocol droid aside from coloring looks the same. 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.
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.
Senator Organa's ship, Tantive IV, is commanded by Captain Antilles. 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.
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.
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.
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.
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.
Summary. Darth Vader's failure to recognize Leia as his daughter in Star Wars: A New Hope stems from George Lucas's late decision to make Luke and Leia siblings. Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection.
While it is no secret that, aside from Jar-Jar Binks, C-3PO is perhaps the most hated character within the Star Wars universe as he constantly complains and treats the much more useful R2-D2 terribly.
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.
The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan. Surely complicating matters is that various characters have referred to him as Obi-Wan in her presence.
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.
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.
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.
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.
After C-3PO and R2-D2 landed on Tatooine, Jawas picked up the two droids, fitting them with restraining bolts. The Jawas sold the robots to Owen and Beru Lars and their nephew Luke Skywalker, a seemingly minor event that would change the fate of trillions in the galaxy.
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.
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.
