"Obi-Wan Kenobi...! Obi-Wan... Now there's a name I've not heard in a long time... A long time. [...] I haven't gone by the name Obi-Wan since, oh, before you were born." So he shoulda started going by Ben during the Clone Wars/during ROTS. There's no implication Owen hung than name on him or it's an "undercover" name for on Tatooine. Owen knows he is/was a Jedi Knight, so his "wizard" pejorative isn't from ignorance but dislike, as you indicate. We've seen a little of the bad blood in the comics, but I'm hoping that gets dealt with -- and well -- in this series. That Owen blames the Jedi in general or Anakin specifically for things, and that gets transferred to Ben.
I wish George had both remembered his own lore that he established in Star Wars and had (or had kept the sef-awareness to seek) the writing chops to paint his way back out of the corner(s) he painted himself into. And also that he'd given the story the room it needed to grow organically. Cramming the excerpts from The Adventures of Obi-Wan Kenobi into three films (and needing a whole separate series to cover the central event of the Clone Wars). Better handling of Yoda's appearance, of Anakin's fall, of the spread-out-ness of galactic events. The Empire had been a recent development as of the events of ANH -- like, within the last decade. Popular with some, unpopular with many who felt powerless to do anything about it. The Jedi purge had happened prior. And the Clone Wars, like the Punic Wars, were a series of related conflicts that spanned decades with lulls between flares. I would have been nice to have Obi-Wan start going by Ben somewhere in there, to maintain continuity with the one film whose story should remain the most inviolate, as everything since owes its existence to Star Wars.
So, now, when we have Anakin's fall, the Empire declared, the Jedi purged, the end of the (brief, singular) Clone War, the birth of the twins (whose existence as twins is spoiled, along with Vader's and Yoda's identities), and Obi-Wan (who has never been called Ben) going into self-imposed exile... all happen on the same day, "I haven't gone by the name Obi-Wan since, oh, before you were born" just got squeezed out.