Theory 1: Leia Doesn't Remember Ben Is Obi-Wan Throughout her encounters with
However, when Luke breaks Leia out of her cell and says, “I'm here with Ben Kenobi,” and Leia doesn't miss a beat. She knows that's his other name. It now seems like her sending the hologram saying “years ago you served my father...” was her way of covering up their personal connection.
Obi-Wan came to the Death Star to save Leia from the Empire's clutches, but was killed by Darth Vader while the others were busy escaping. Leia didn't see Obi-Wan again, nor did she experience any sadness when she learned of his death.
We know from Leia's parents and from moments in the Star Wars sequels that she was, in fact, Force-sensitive, even though she didn't get a chance to display those powers in the original trilogy.
She doesn't bat an eye, shows absolutely no emotion. Luke is devestated but she is cold, like she never knew Obi-Wan.
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.
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.
In Death Star, it seems the Sith Lord could have discovered Leia's true identity if he'd pursued his hunch. However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter.
The reason Darth Vader could sense Obi-Wan and Luke was because of how they actively used the Force several times throughout the Original Trilogy. Vader never sensed Leia because she didn't the Force; Leia did not even know she had Force powers to begin with.
There are a lot of hints given throughout the Star Wars franchise that Padmé Amidala was in fact Force sensitive. It is clear that the young queen and later senator from Naboo was not strong in the Force or trained in the ways of the Jedi, but she very likely still had some low-level sensitivity.
She's important in the plot sense because Reva, who is searching for Obi-Wan for Anakin, uses Leia as bait but she's also important because she reminds Ben what he lost in Padmé and Anakin but what he gained in the twins. Leia is just as important as Luke.
With Leia, Luke, and Darth Vader all being major characters in "Obi-Wan Kenboi," the show is having to tread lightly as the "Star Wars" canon is pretty explicit. We know exactly when Vader discovered that Luke was his son, and we know when he figured out that Leia was connected to him as well.
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.
Why does Obi-Wan Kenobi age like that? Because he's not real, and is a fictional character played by different people. You see, Obi-Wan Kenobi is played by Alec Guinness in the original trilogy. Guinness was 62 when he filmed A New Hope, and he died in 2000.
The first time, Obi-Wan tells Leia she reminds him of someone “fearless and stubborn,” a “leader who died a long time ago.” While it's possible he was referring to Satine Kryze (voiced by Anna Graves in the Clone Wars animated show), it seems more likely he was talking about Padme.
She looks at the names on the wall, lingering over an image of the Jedi Order crest. She then screams in rage, tossing some things that were hiding the control panel to the secret door. She then is able to enter the tunnels and get ahead of young Leia as she flees to the ship.
Nope. Luke, unlike Leia, never really had a father figure in the first place. Leia never was saved by Darth Vader the way Luke was, and never understood Luke's forgiving him. She hid her identity as Darth Vader's daughter, and identified as Bail Organa's daughter.
Vader learned that Leia was his daughter by sensing it from Luke in Return of the Jedi.
However, she chose not to tell Anakin, presumably because he was about to go into a battle. Anakin was prone to letting his emotions affect him, and knowing that Padme was pregnant would've thrown him completely off the task. And Padme probably didn't think that her husband would be fighting battles for months to come.
Leia Organa-Skywalker
Leia Amidala Skywalker (portrayed by Carrie Fisher) is the wife of Han Solo, the mother of Ben Solo, the younger twin sister of Luke Skywalker, the daughter of Anakin Skywalker and Padmé Amidala, and the granddaughter of Shmi Skywalker, raised by Bail and Breha Organa of Alderaan.
What would happen if Darth Vader came across R2-D2 and C3PO? He came across Threepio on Bespin. 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.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
In the post-2014 canon universe, the story that reveals Darth Vader discovering Luke Skywalker's identity (and thus the fact that the Death Star's destroyer is his son) is issue 6 of 2015's Star Wars comics by Marvel, which takes place sometime shortly after A New Hope.