Perhaps, the old creature simply forgot. Late in the film, Darth Vader does not recognize C-3PO who is in Cloud City with Han Solo, Chewbacca, and Leia. Although C-3PO is not completely assembled in the scene, he is definitely visible to Vader.
He either didn't realize it was the same protocol droid or figured he'd been memory-wiped so FUNCTIONALLY wasn't the same droid and didn't care.
He does. In the comic Star Wars Tales #6, we see an interaction between Vader and C-3PO. In the comic, Boba Fett brings Vader C-3PO's remains. Vader instantly recognizes C-3PO, and is reminded of his childhood.
When R2D2 was missing in action, Anakin went to great lengths to rescue him, even distrusting his replacement droid, which turned up to be a mole planted by General Grievous. R2 was on Mustafar when Anakin became Vader. That, perhaps, explains that he doesn't try to reacquire him.
So Owen had no idea his "new" protocol droid's name was C-3PO. A counter to that might be asking why Owen didn't recognize C-3PO's distinct voice, but again, it's worth remembering Owen hadn't seen C-3PO in more than 20 years. It's possible Owen simply forgot what C-3PO's voice sounded like.
Obi-Wan Kenobi has no idea who C-3PO is when they meet in “Star Wars: A New Hope” even though the prequel trilogy later told us that the two certainly knew each other.
Obi-Wan Was Pretending He Didn't Know R2-D2
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.
Yoda recognized R2-D2 during The Empire Strikes Back.
Darth Vader can not use force lighting, because of his severed arms. Robotic hands can't summon the force lighting. However Darth Vader can still use other forms of the force, such as force choke.
Both R2D2 and C3PO both know that Darth Vader and Anakin are one and the same. 3PO's memory was erased back in Star Wars Episode III: Revenge of the Sith but was restored by R2 back in Star Wars Episode IV: The Rise of Skywalker. As such, they both remember everything that happened.
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. 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.
Vader agreed to help the handmaiden, silently recalling the time he spent with Padmé in the process. In this moment, he was once again Anakin Skywalker, a young man in love who simply wanted to change the world for the better.
In "The Empire Strikes Back," Darth Vader stops Boba Fett from shooting Chewbacca because he has plans for the Wookiee.
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.
C-3PO accidentally became part of the Battle of Geonosis when his head was affixed on top of a battle droid's body after a mishap in the Geonosian droid factory. R2-D2 and C-3PO witnessed the secret wedding between Anakin Skywalker and Padmé Amidala on Naboo.
Darth Vader only learned he had a daughter in Return of the Jedi - but there's no evidence he realized she was Leia before his death and redemption.
1 Darth Sidious
There has been no Sith, as powerful, meticulous, nor as evil as the Emperor himself, Darth Sidious. As previously mentioned, Sidious trained in the Dark Side by Darth Plagueis before Sidious killed Plagueis in his sleep, making Sidious a Sith Master.
Grandmaster Yoda himself was capable of summoning force lightning in the form of Emerald Lightning. Galen Marek was an extremely skilled user of this Force power, even after his conversion to the light side, rivaling Darth Sidious.
It's likely Kylo never learned how to summon Force Lightning
From what we learned from the Marvel Comics story on Kylo Ren and his upbringing, along with the information explained and even alluded to in the sequel trilogy — it's entirely likely that Kylo never completely learned how to harness Force lightning.
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.
R2-D2, the indomitable droid and mainstay of the Star Wars series, may be responsible for one more incredible feat: saving Grogu.
Obi-Wan's Early Years
“I was identified as Force-sensitive and taken to the Jedi Temple on Coruscant.” In Marvel's Obi-Wan comic, we get a glimpse at his childhood there as a youngling. He began training under Master Yoda as a youngling until Qui-Gon Jinn chose him as an apprentice when he was 13 years old.
While, it may be true Chewbacca met Yoda and Ahsoka, there is no indication that he met Anakin. Even if Chewbacca has met Anakin, Chewbacca would have assume Anakin was one of those Jedi killed in Order 66.
It's because of his mastery of sorsue (sorry for my bad spelling.) Well if you want the ACTUAL reason it because in the original 3 films the Green Light Sabre didn't exist until after Obi Wans death.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.