In a new interview with Gizmodo, Obi-Wan Kenobi director Deborah Chow confirms that at the beginning of the series Obi-Wan still believes Darth Vader died on Mustafar ten years ago.
“[Obi-Wan] believes he killed [Anakin] at the end of Revenge of the Sith,” says Chow. “I think that’s something that’s sometimes a little bit overlooked, but it’s quite significant. So for us, on the show, he doesn’t know [Anakin is alive] yet.”
This means that Obi-Wan has really been quite ignorant of what was happening in the Empire during his years of exile on Tatooine.
Nevertheless, that’s an interesting choice and I look forward to seeing how he’ll learn the shocking truth.