I'm not buying that he's not heard of darth vader though in the 10 years or whatever it is. but never mind, doesn't really matter.
It all depends on how much you want to take separate pieces and fit them together to draw a conclusion you are satisfied with.
If you follow the Darth Vader comics, it seems Vader's initial time is spent consolidating his position within the Empire, not just as the apprentice of Sideous, but as the second in command of the Emperor. There's a newly established Imperial officers' corps to bend to his will and a lot of internal politicking going on. After that he personally hunts Jedi until the Emperor orders him off. Presumably that's left these inquisitors hunting the dregs.
The whole point of hiding out on Tatooine is that it's isolated. Obi-wan has cut himself off from the force, and the world outside. Just as it's unlikely word of him will leak to the outside if he just stays hidden, it's equally likely very little other than rumour will make it to Tatooine. I'm sure there is news to be had if one goes looking for it, but Obi-wan isn't looking for it. He'll know of inquisitors in some vague form, but might assume they're acting at the direction of the Emperor.
He might suspect Palpatine has an apprentice or deputy, but might not realise it's Vader/Anakin. I agree it's stretching things, but that's how I choose to interpret it.
That irked me as well. They later explained it with her saying that 'I found a link between them in our data files' or something. Pretty lame explanation.
Otherwise I am really enjoying the series, Ewan McGregor is great as Obi-Wan as always. After the sequel trilogy best to keep your expectations low and then when something like Mandalorian comes along it is an unexpected treat.
We know Reva is a force user; perhaps he obsession with Kenobi guided her search through the records. It can't be that difficult to look up news reports from 10 to 15 years ago on the SW equivalent of the internet, and force intuition might have told her Kenobi's connection with Bail Organa was stronger than most. Lots of force sensitives are good at playing hunches. I do wonder, though, what would have happened with Leia if Reva's hunch about Kenobi still being alive was wrong. Probably sold into slavery or some such.
