Sauron Lives

Annatar was a name he picked up in Eregion working with the elves.

And Gorthaur is a Sindarin name, also given him by the Elves, and meaning largely the same thing as Sauron etymologically.

I thought that him referring to himself in third person was an excellent touch. Probably the most powerful way to do the revelation. I'm so glad it wasn't "It's a-me! Sauron!"

I think his favorite is Tar-Mairon. Or maybe Aulendil.

There he's spelling out the elf thought where he's only known by that name, which is an insult. "This is what they will say."

Annatar was a name chosen by himself, and the Sindar named him Gorthaur.

You are right about the mistake they did in the first episode.

And he was called Halbrand in the TV show

I like how he turned around her boast that she was older than the sunrise by saying I awoke before the breaking of the first silence.