Obi-Wan knowing Anakin took the name Vader doesn’t mean he knew that Vader survived past their fight in episode 3 though, right? The fair assumption would be that the guy you left chopped up and on fire did in fact die from those injuries. Isn’t that the surprising information, and not that Anakin changed his name? I haven’t seen it, but that’s the impression I got.
If you had been set to write an Obi show and had gone back and refreshed yourself on the canon - scenes and dialogue made in both PT and OT - would you have written Obi as unaware?
You’ll think I’m just being contrarian, but yes, I would have written have written Ben as unaware. He needs to believe he was successful in ROTS, otherwise it calls into question why he hasn’t done anything about Vader in the intervening years. More importantly, if you’re writing something in this gap, you would want to show him finding out the truth as it is good drama. I’m sure there is a bunch of stuff I’d do differently, but this particular thing seems pretty logical.