Leia doesn't get to reunite with Obi-Wan, and instead, just before escaping with Han and Luke, she sees his murder. Of course, Leia doesn't know Darth Vader is her father yet, either in A New Hope and certainly not in Obi-Wan Kenobi. But for the most part, the narrative focus of A New Hope is on Luke.
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.
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.
Prior to this series, it never made a lot of sense why Leia would've named her son after Ben Kenobi, the mentor of her brother whom she never met.
Because they made that movie four decades before she got to know him in the latest iteration of “The Lore Between the Lore" that Disney+ is selling us. The same reason she didn't show a big reaction when the her entire planet and all those she was responsible for died in an instant.
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.
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.
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.
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.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
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.
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.
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.
The calculation is a good example of the physics phenomenon, the twin paradox. which states that twins travelling relativistically appear to age differently to one another due to time dilation.
It's not just about the rescue. In episode two, Leia reminds Obi-Wan of someone "fearless and stubborn" that he used to know. Not a Jedi, but "a leader." Kenobi is of course talking about Padmé Amidala, Leia's biological mother, but she doesn't realise that at this point.
When Organa reminds him, “What about your duty to his sister?” Obi-Wan's mind changes, and he agrees to help. He finds and rescues the young Princess Leia, but their journey back to Alderaan is not an easy one. Throughout multiple narrow brushes with death, the two rely on each other for comfort and strength.
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.
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.
Vader learned that Leia was his daughter by sensing it from Luke in Return of the Jedi.
While in Tatooine's seedy Mos Eisley cantina, Chewbacca met Obi-Wan Kenobi, who was looking for passage to Alderaan. Chewie arranged a meeting between the rogue smuggler, the Jedi, and Luke Skywalker.
Vader is aware of the existence of Leia Organa, but does not know that she is his daughter. And he initially has no knowledge whatsoever of Luke. He learns Luke's identity after A New Hope, before Empire Strikes Back.
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.
Has Leia 'forgiven' Anakin Skywalker for his crimes as Vader? Yes, in the “Legends” part, she even named her third child for him, as a symbol of his heritage and redemption. However, it's more than acceptance that Anakin is her BIOLOGICAL father and she got her personality and Force sensitivity from him.
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.