C-3PO doesn't remember Anakin because his memory was wiped at the end of Revenge of the Sith by Bail Organa to protect Luke and Leia, erasing his experiences with Anakin Skywalker, his original creator, and his time with Padmé Amidala, dorksideoftheforce.com. While R2-D2 retained his memories, C-3PO's wiped memory left him oblivious to Anakin's dark turn as Darth Vader, though his memory was restored by the end of the sequel trilogy.
Neither C3PO or R2D2 ever got to know Darth Vader. Nor would they hve been able to recognize anything about Vader that would have indicated that he was once Anakin Skywalker. Moreover, C3PO's memory was wiped clean after the twins were born. Thus he would no longer have any memory of his former “maker” either.
As can be seen in the movies, c3po is not the only protocol droid and they look very similar. Same with R2D2 he isn't the only blue astromech droid. The droids and galaxy all believe Anakin is dead. So there is no reason for the droids to know vader and no reason for Vader to recognize the droids.
No, Darth Plagueis is not Anakin Skywalker's biological father, but there's a strong theory (especially in Star Wars Legends and early drafts) that his experiments with midi-chlorians to create life led the Force itself to create Anakin, the Chosen One, as a reaction, making Plagueis the "unintentional father" of the prophecy. In current canon, Plagueis is a legend Palpatine uses to lure Anakin, and the exact nature of Anakin's conception by the Force remains a mystery, though he had no conventional father.
At the end of Revenge of the Sith C3PO's memory is wiped to protect the twins. R2 retains memories but doesn't explicitly state the history he and Obi Wan has. C3PO is perplexed by the way R2 is acting while trying to get to Obi Wan in A New Hope because of the memory wipe.
Plot convenience. If 3P0, who could talk, remembered, then there'd be a gaping plot hole for why 3P0 didn't recognize the name “Skywalker” and tell Luke everything. But, since R2 couldn't talk, Lucas could pretend that R2 couldn't tell Luke even though episodes 5 and 6 implied they could communicate.
Qimir has already been calling himself Darth Venamis, and is ready to officially be a Sith Lord Apprentice, but, is also already conspiring to get a pupil of his own, & eventually kill his own master as well.
Matthew J Meyer George Lucas has stated: "Anakin Skywalker was conceived by the midi-chlorians, but it was Palpatine who manipulated the midi-chlorians to create Anakin" (Source: "Star Wars: Episode III - Revenge of the Sith" DVD commentary, 2005).
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.
To answer your question R2 saw anakin die and did not see vader face to face until tantive iv at no point was he privy to vaders secret While with bail organa.
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.
Though there was some debate among the fans that Anakin Skywalker's son, Luke Skywalker, was actually the Chosen One since he caused his father to destroy Darth Sidious, the debate was settled when George Lucas himself confirmed in an interview that Anakin, even after becoming Darth Vader, was still officially the ...
Anakin Skywalker, one of the main characters in the "Star Wars" films, meets the criteria for borderline personality disorder (BPD).
Vader breaks free of the operating table and takes a few steps before doing the only thing anybody in his position could do, he screams an unholy, bloodcurdling scream. His vocal computer has nothing close to this sound in its database so it translates it to the infamous 'Noooooooooo'.
Essentially he was a Sith Hobbyist or something. Darth Maul is the weakest. Bane was strong : he killed all the Sith and lots of Jedi.
During the High Republic Era, Plagueis was actively working against the Jedi. By 132 BBY, he had taken on a former Jedi—a human known as "the Stranger" or by the pseudonym "Qimir"—as his apprentice.
In a study published in the journal Psychiatry Research, French psychologists and psychiatrists determined that Darth Vader had six of the nine criteria used for a BPD diagnosis, as defined by the Diagnostic and Statistical Manual of Mental Disorders (DSM): Impulsivity. Rage and anger management issues.