A) Neil Gaiman was heavily, heavily involved in the making of the show and made the change as there were constrictions on using "John" by Warner (he's been used in other series recently and I think there's some legal entanglements there.
B) Johanna wasn't a cockney. you'd know if she was a cockney.
C) I thought the show was a pretty faithful adaptation, there were always going to be technical limitations on what can be can (Sturridge makes a good Morpheus, even if he's not bone-white with star-eyes.
D) Directors don't change characters, the writers do. Producers may influence the writing direction, but at the end of the day, the showrunner (head writer) is the one that actually dictates the show's story. Directors are only responsible for the episode they are directing., much the same way actors only say lines and don't improv the whole thing.
Oh, and if you start thinking that the TV show is "woke", you have never read the comics.
Personally, I enjoyed it.