After Anakin falls to the dark side of the Force and becomes Darth Vader, he takes R2-D2 with him when he goes to assassinate the Separatist council, but tells him to stay with the ship.
Yes he did. And the saddest thing is that there was nothing he could do about it. He was broken. The first case is shortly after ROTS when Vader was making his Sith lightsaber.
Remember that this is the first (and only) time Vader saw C3PO after RoTS. Threepio was getting pushed into an escape pod by R2D2 by the time Vader entered their ship in ANH. Though he was chased throughout the original series, this was the only time Vader actually saw Threepio, again.
Yoda recognized R2-D2 during The Empire Strikes Back.
Star Wars Characters That Can Understand Droids
While all droids understand Binary, only a handful of living creatures can. Canon characters, such as Anakin Skywalker, whose relationship with R2-D2 is one of the best in the whole series, Rey, Poe Dameron, Hera Snydulla and Kazuda Xiono are fluent in the droid language.
After the battle, R2-D2 and C-3PO were the sole witnesses to the marriage of Anakin Skywalker and Padmé Amidala in Lake Country. After this Padmé gave ownership of R2 to Anakin while she kept 3PO.
R2-D2 was present when Padmé gave birth to Leia and Luke, so he knew Luke was Anakin's son – but what he didn't know was that Anakin became Darth Vader. In addition to that, Anakin's fall was surely a painful event in R2-D2's life, one that he definitely wouldn't like to remember or even talk about.
He hasn't owned a droid because R2-D2 is his friend. No one can "own" him, and to claim to have done so disrespects the countless ways the little astromech has saved the galaxy. If the theory applies, then Obi-Wan cleverly makes note of that while simultaneously hiding his past companionship with R2-D2.
R2-D2, the indomitable droid and mainstay of the Star Wars series, may be responsible for one more incredible feat: saving Grogu.
Since Obi-Wan and Anakin often fought together, Obi-Wan was friends with R2-D2 as well. This means that although R2-D2 might not have immediately recognized Obi-Wan on Tatooine due to his age, Obi-Wan should have recognized the droid.
Obviously, C-3PO does not recognize Vader because his memory was wiped at the end of Revenge of the Sith.
Darth Vader can not use force lighting, because of his severed arms. Robotic hands can't summon the force lighting. However Darth Vader can still use other forms of the force, such as force choke.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Summary. First encountered during the final mission of Star Wars Jedi: Fallen Order, Darth Vader is the final boss faced by Cal Kestis, though his boss fight differs significantly in that it heavily relies upon quick-time events.
Original trilogy
The droids then escape in a pod that crashes on Tatooine near Jedi Master Obi-Wan Kenobi's (Alec Guinness) desert abode. R2-D2 and C-3PO are then abducted by Jawas and bought by Owen (Phil Brown) and Beru Lars (Shelagh Fraser), uncle and aunt of Luke Skywalker (Mark Hamill).
Senator Bail Organa takes ownership of R2-D2 after Anakin completes his metamorphosis into a Sith Lord. By proxy, he is the enemy of the Empire, as Organa is a staunch supporter of the Rebellion.
As it turns out, the Jedi who saved Grogu was Kelleran Beq, played by none other than Ahmed Best.
While fans don't know the state of Grogu's well-being in the sequel trilogy, his ties to Mandalore might explain why Kylo Ren doesn't kill him. It's likely Grogu stays with Din Djarin and the Mandalorians, and never returns to embark on his training with Luke.
Grogu Was Saved By a New Character
Yet the Jedi is not a household name, and not someone anybody likely suspected. The door opens to reveal that it is Jedi Master Kelleran Beq standing there, and he helps get Grogu to safety and off Coruscant.
Vader agreed to help the handmaiden, silently recalling the time he spent with Padmé in the process. In this moment, he was once again Anakin Skywalker, a young man in love who simply wanted to change the world for the better.
While, it may be true Chewbacca met Yoda and Ahsoka, there is no indication that he met Anakin. Even if Chewbacca has met Anakin, Chewbacca would have assume Anakin was one of those Jedi killed in Order 66. How would he know who Luke's father was? There is no evidence they ever met, never mind actually knew each other.
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.
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."
C-3PO accidentally became part of the Battle of Geonosis when his head was affixed on top of a battle droid's body after a mishap in the Geonosian droid factory. R2-D2 and C-3PO witnessed the secret wedding between Anakin Skywalker and Padmé Amidala on Naboo.
R2 doesn't know it. It's as simple as that. He isn't present on Mustafar (he flies with Anakin but is ordered to stay at the ship. He isn't present while the slaughtering of the seperatists or the fight of Anakin/Obi-Wan.), differently to Obi-Wan and C-3PO.