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.
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.
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.
However, rather than be an oversight or plot hole, Leia might not have remembered old Ben for one sinister reason. This has to do with Ben's Jedi powers, namely the mind trick. As he grew older, he'd use it on Stormtroopers to protect Luke Skywalker.
To say the truth, that was because Luke and Leia never knew they were “siblings,” let alone twins. They wouldn't even know until midway through Return of the Jedi.
Leia is annoyed with Han, who insists she has feelings for him, so she kisses Luke to prove she doesn't. Presumably, the scene was simply meant to make Han jealous.
Darth Vader may have never known Princess Leia was his daughter in Star Wars and never cultivated a relationship with her, even when he was a Force ghost. Anakin Skywalker never knew Padmé was pregnant with twins, and he believed his child had died with his wife.
For all we know, Leia specifically channeled her own life force into Ben, helping Rey along and sacrificing herself in the process. That may be why Leia finally dies and fades away at the moment Ben revives Rey and fades away himself. When Ben dies, any tether Leia still had to the living world went with him.
“So Leia Force projects herself as Ben and uses her life force to save Rey. Even going as far as to kiss Rey to convince her it's Ben. It's why when Ben disappeared, so did Leia.”
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.
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 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.
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.
On Tatooine, the droids are captured and sold to Luke Skywalker's uncle. As Luke is cleaning R2-D2, he accidentally triggers part of the message from Princess Leia, which plays on repeat. "Help me, Obi-Wan Kenobi," she says, "you're my only hope."
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.
Does Darth Vader know Leia is his daughter? Vader learned that Leia was his daughter by sensing it from Luke in Return of the Jedi. Vader learned about Luke after he sent Boba to capture Luke alive, but he escaped and Boba only managed to learn his name: Skywalker.
Why Did Rey Bury the Lightsabers? Since Luke and Leia, her masters, have become one with the Force, this is her way of honoring them by putting their weapons to rest. It also shows that Rey is burying the past while carrying it with her — both in her spirit and in the lightsaber she now wields.
Following Palpatine's final defeat and her own resurrection, Rey adopts the name Rey Skywalker to honor her mentors and their family legacy and renounce her lineage. As the last remaining Jedi, she makes it her mission to rebuild the Jedi Order.
Do Rey and Kylo have kids? She does not have a baby bump, her hand never goes to her stomach to indicate she's carrying a child, and there wasn't exactly any time for her to have conceived a child with anyone in the course of the film, including Kylo Ren/Ben Solo.
For their heroism in destroying the Death Star, Han Solo and Luke Skywalker receive the Medal of Yavin from Leia Organa in a ceremony on Yavin 4. Decades later, Maz Kanata gives Chewbacca the medal once worn by Han, which Leia was holding when she died.
“While it is not demonstrated in the film, the twins will actually have aged very differently due to their extensive travelling at speeds close to that of light. “Despite Luke's journey being twenty five times longer than Leia's, the time dilation he experienced was only around ten times larger.
Leia's journey yields a time dilation of 62.6 days; however Luke experiences a time dilation of 700.8 days (1.92 years). The students concluded that Luke is therefore 1.75 years younger than Leia, possibly rendering them the first twins ever to have over a year between their ages.
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.