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.
Leia didn't see Obi-Wan again, nor did she experience any sadness when she learned of his death.
In A New Hope, Obi-Wan and Leia never spoke face-to-face, only communicating through Leia's recorded message to the former Jedi Master.
She doesn't bat an eye, shows absolutely no emotion. Luke is devestated but she is cold, like she never knew Obi-Wan.
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.
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.
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.
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.
In A New Hope, Leia's utter faith in Obi-Wan Kenobi comes circuitously from her father, who, in that film, is never glimpsed. 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.
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 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.
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.
While the events of Star Wars: Bloodline explain why Leia did not name her son after her biological father, Obi-Wan Kenobi makes Han and Leia's decision to name their son Ben far more understandable. In "Part I," mercenaries hired by the Third Sister, Reva, kidnap Leia to draw Obi-Wan out of hiding.
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.
After the Battle of Endor, Leia trained as a Jedi with Luke, but left the Jedi path after sensing it would result in the death of her son.
Even though he had a fierce confrontation with Leia Organa during the opening scenes of 'Star Wars Episode IV: A New Hope,' he never even suspected she was his daughter. That was why the only person Vader targeted and tried to convince to turn to the dark side was Luke, as he didn't even know that he had a sister.
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.
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.
Padme didn't have any force powers and she was too old to become a Jedi. She may have had some kind of force powers whilst pregnant with Luke and Leia but being with Anakin could have caused some force sensitivity at the time.
Similarly, her rebellious, rule-breaking and trouble-making nature resembled Anakin more than Padmé. However, both parents were adventurous and stubborn people. Thus far, her leadership skills are the one thing missing from Leia's portrayal in Obi-Wan Kenobi. It's well justified since Leia is still a child.