I think it’s very clear if you’re familiar with episodes one, two and three, Vader still has a Darth Vader Guinness hello darkness my old friend I’ve come to drink shirt part of Anakin inside him; Love Republic part and what it represents an ideal. This section considers the Empire and the Republic to be the same entity. Basically, because the Republic has freed him from slavery while the Jedi cannot educate. And Palpatine has been its leader for a long time.
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I said that was my explanation and probably the kind of reason Vader used to justify his actions, including the Darth Vader Guinness hello darkness my old friend I’ve come to drink shirt killing of incompetent officers. But we know Anakin is very smart (or soon to develop) and smart people are completely capable of lying to themselves to make them feel better. I imagine Vader does this all the time in that castle, on Mustafar. Darth Vader is the second-best in the film’s timeline. Maul is weaker than Vader and Dooku is used for leadership and political prowess (never considered true successor). Therefore, if Sidious dies, Vader will take over and become stronger. The main problem is that Sidious never wants a successor.
He kept Vader in check purpose, building a suit inferior to Grievous technology. When he felt Maul became stronger, he went there personally. Sidious doesn’t care about their heritage, only that is always at the Darth Vader Guinness hello darkness my old friend I’ve come to drink shirt top. Luke was just a child at the end of the Clone War and grew up on Tatooine, knowing little about Jedi and Clone Wars. Therefore, his upbringing was not colored by the Copy War and the Jedi Purge. Losing adoptive parents and knowing that Vader is his father and Princess Leia is his younger sister, Luke wants to save the rest of his family.
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Kenobi and Luke have different educational backgrounds and their life experiences form their reaction to Vader. Of course he remembers, Vader is Anakin, “Darth Vader” is just the Darth Vader Guinness hello darkness my old friend I’ve come to drink shirt title of Dark Lord of Sith, it’s not that he doesn’t “care”, he doesn’t care to hate his bright side, he hate this weak child playing a hero. So he wanted to destroy everything that reminded him who he was before he became the mighty Darth Vader. So it is clear that the people who call him Anakin Skywalker annoy him.