Senator Organa, Obi-Wan, and Yoda, due to a misunderstanding between Padme's death and Anakin's, plan to disguise the births of Luke and Leia as having died with Padme so that the Emperor will not find them.
Misled through Obi-Wan that Vader, the emperor's new apprentice, was dead, the three of them hid Luke and Leia in Alderaan and Tatooine under the assumption that Vader would not find them.
The problem is that the emperor will be looking for them. So Alderaan in the core adopted Leia, who was not named Skywalker, to Senator Organa. They figured that the emperor wouldn't mind having Luke on Tatooine in the Outer Rim under the name Skywalker.
However, Obi Wan confirms on the holonet that Vader was alive after he left Yoda and Organa. There, he became constantly concerned about Vader's proximity to Tatooine.
Fortunately, Vader did not go to Tatooine.
Organa, on the other hand, wasn't too worried. Leia's name wasn't Skywalker. The problem is the two droids.
After the end of the Clone Wars, Vader went to Alderaan. Vader thinks the child is dead and mistakenly assumes that Leia is Organa's real child, but if the droids are seen, Organa is in danger. If they saw R2's memory, they would know that Luke and Leia existed, since R2's memories have not been erased. However, this does not necessarily mean that Vader will report it to the Emperor. Vader would want to train her as his apprentice because he has ambitions to defeat the Emperor. If the emperor guesses, he can only turn over Luke, the name of Skywalker, and if he does, he can turn over Leia in secret.
And you can take Leia as your apprentice in secret. The emperor would not expect Anakin's descendants to be twins. At worst, if the emperor gets wind that Leia is a descendant of Anakin, as a Sith based on the principle of two, he will still be unsure of what to do with his apprentice.
My guess is that the evil emperor will allow Vader to take Leia as his apprentice, and once trained, he will want to play Luke versus Vader and Leia, with the winner on his side.
It would be hard for a father to have his children fight each other. Therefore, he will confide in Luke and Leia that they are twins. Then Luke and Leia would refuse to fight and would side with their father, becoming a real threat to the emperor.
Thinking of this, Yoda has Obi Wan confide in Luke that he and Leia are twins.
On the condition that Luke is convinced that he is Vader's son in order to be a threat to the emperor.
Before that, Leia would have realized that Organa was not the father when Luke told her that they were twins. Translated with www.DeepL.com/Translator (free version)
