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.
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.
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. That explanation holds the most water for a number of reasons.
R2-D2 witnessed some of Anakin's best moments and knew him when he was an innocent boy on Tatooine; it might have been healing for Luke to hear these stories. Perhaps, like the stories about Padmé, they were simply too painful to share.
One of the mysteries from the original trilogy that was fueled by the prequels is why R2-D2 never told Luke that Darth Vader was his father, as he actually knew Anakin Skywalker and witnessed his turn to the dark side.
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.
During the Clone Wars, it was common practice to wipe the minds of astromech droids after every mission to avoid the risk of Separatists taking valued information. But Anakin remained staunchly against this idea for R2-D2, meaning the droid never had to worry about losing the memories of his past.
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.
Because as far as he knows it's just a generic protocol droid. There are millions of them all over the galaxy. He has no reason to think this droid is the same one he was briefly acquainted with many years ago.
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.
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.
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.
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.
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.
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 name derives from when Lucas was making one of his earlier films, American Graffiti. Sound editor Walter Murch states that he is responsible for the utterance which sparked the name for the droid. Murch asked for Reel 2, Dialog Track 2, in the abbreviated form "R-2-D-2".
After decades of missions with R2-D2, Luke Skywalker was reasonably fluent in droidspeak. The most common way for binary droids to communicate with organics was by writing, conveyed via another computer system. This is how astromech droid copilots would speak with the pilot of a starfighter.
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.
