He did everything he could to forget his past. Also, his plating had been replaced many times, and protocol droids all look very similar. It's like if you sold your car and saw it 20 years later with a different pain job; you wouldn't recognize it.
He was also evasive with Luke as far as his relationship with Luke's father. 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.
The real reason why Obi-Wan Kenobi, the Lars family, or Darth Vader didn't act in the original Star Wars trilogy as though they knew C-3PO or R2-D2 previously is that the prequel trilogy, in which they first meet the two droids, had not been written yet.
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.
As has been noted in several instances, Artoo has never had a full memory wipe, enabling him to retain his recollections of everything he saw and heard over the decades. This includes his first meeting with Padme Amidala, a nine-year-old Anakin Skywalker, and C-3PO himself during the events of The Phantom Menace.
Why Didn't Darth Vader Remember C-3PO in The Empire Strikes Back? Star Wars Explained (Legends)
Why doesn't Darth Vader recognize C-3PO and R2-D2?
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.
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 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!
C-3P0's memory was wiped at the end of Episode III so if he wasn't told he had no idea that his maker was the future Darth Vader. R2-D2 remembers it all and if I had to guess he is quiet sad about Anakin's turn to the dark side.
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.
Remember that this is the first (and only) time Vader saw C3PO after RoTS. Threepio was getting pushed into an escape pod by R2D2 by the time Vader entered their ship in ANH. Though he was chased throughout the original series, this was the only time Vader actually saw Threepio, again.
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.
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
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.
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.
A smart, spunky droid who would serve a multitude of masters over his lifetime, R2-D2 was never given a full memory wipe nor did he ever receive new programming, with these factors resulting in an adventurous and independent attitude.
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.
Unfortunately, Rex and Vader never meet again though. Why didn't Palpatine feel afraid of showing his evil actions, behaviors and ways to Anakin and the Jedi anymore?
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.
