Vader was hunting down the pilot who blew up the Death Star, and hired Boba Fett to find them. Boba was unable to, but he did give Vader a name: “Skywalker.” This, combined with his knowing Luke was Force-sensitive and had been trained by Obi-Wan, was what made him realize the truth.
He knew Luke was, but not Leia at first. In the first two Star Wars films, Vader comes face to face with her multiple times and doesn't recognize her as his daughter. As for Luke, he knew from the moment he heard the name he had a son and tried to find him.
In this comic issue, Darth Vader is informed by Boba Fett that the Rebel pilot who destroyed the battle station (and briefly battled Vader on Cymoon 1 in issue 2) is named Luke Skywalker, who Vader immediately recognizes as his son.
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
Vader finds out Luke is his son - Empire Strikes Back (1980)
Does Vader ever find out Leia is his daughter?
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. 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.
Yes, they did. Eventually, Leia contact her good friend Pooja Naberrie to discuss her mother so they definitely knew about Padmé Amidala and the fact she was their biological mother. did luke and leia ever figure out who their mother was?
Luke and Leia never sensed that they were twins until Return of the Jedi despite both being sensitive to the Force. Anakin Skywalker's twin children are the original Star Wars trilogy's driving force, having been separated after Padme's death.
And during the conversation, Padme is holding her stomach and appears to have a bump, seemingly confirming she was pregnant long before Revenge of the Sith. However, she chose not to tell Anakin, presumably because he was about to go into a battle.
Returning to Dagobah to complete his training, an ailing Yoda told Luke the terrible truth that Vader was his father, Anakin Skywalker. Rather than destroy his father, Luke sought to bring him back into the light. At 900 years old, Yoda passed away, telling Luke that there was another Skywalker.
Shmi informs Qui-Gon that Anakin has no father, leading Qui-Gon to suggest that Anakin is a product of midi-chlorians (Force-imparting microorganisms). As the film progresses, Anakin leaves Tatooine to begin his Jedi training.
The two recognize Luke's similarities to Anakin and try to prevent him from sharing his father's fate, but they let him remain Luke Skywalker instead of having him go by Luke Lars out of respect for his grandmother, Shmi Skywalker.
Han Solo marries Princess Leia and they have three children: twins named Jacen and Jaina, and a younger son named Anakin. Luke reestablishes the Jedi Order, marries a non-movie (but fan favorite) redheaded Force-wielder named Mara Jade, and they have a son, Ben Skywalker (named in honor of Obi-Wan “Ben” Kenobi).
In Part III, Leia revealed her knowledge about the adoption, only that she didn't know about her birth, which explained her unsurprised response when Luke told her that they were brother and sister in Return of the Jedi. Obi-Wan Kenobi also provided an explanation about how Leia gradually "lost" her Skywalker heritage.
The marriage, witnessed by the droids C-3PO and R2-D2, was kept secret due to Amidala's place as a prominent Senator in the Galactic Republic and because of Skywalker's membership in the Jedi Order; the Jedi Code prevented Jedi from falling in love and forming attachments such as marriage.
Her body was made to still look pregnant in order to keep Luke and Leia safe from their father, Darth Vader, the Dark Lord of the Sith formerly known as Jedi Knight Anakin Skywalker, who fell to the dark side of the Force in a failed attempt to save his wife from dying.
Presumably, the scene was simply meant to make Han jealous. Still, Luke looked very thrilled by this unexpected turn of events and Leia seemed to consider both men romantically, though the sexual tension with Han was admittedly much more palpable.
While the kiss was simply intended to make Han Solo jealous, the full implications of the encounter became even more problematic when Leia is revealed to be Luke's twin sister during Return of the Jedi.
Star Wars Theory: R2-D2 Didn't Know Anakin Skywalker Became Darth Vader. R2-D2 served Queen Amidala and later Anakin Skywalker, accompanied by C-3PO. Unlike the golden protocol droid, R2-D2 never had a full memory wipe, so he was well aware of all events that happened around him.
Leia is remembering Padme but the images she sees are due to her force sensitivity, to quote Yoda in Empire "Through the Force, things you will see. Other places. The future...the past...old friends long gone." This could suggest that Leia is confusing Force visions with memories.
Given that she's the child of Anakin Skywalker, who's prophesied to be the Chosen One, the Skywalker bloodline holds a tremendous amount of power. With Leia's strong connection to the Force, it seems like the most likely solution to this inconsistency is that she's caught glimpses of her mother through Force visions.
