Will there be privacy in TESO and options to stay invisible or better yet, decide if others can see your account name? Or will it be like some recent games where everyone who ever friends you can always see when your online?

As soon as the NDA is lifted up, I'll be glad to answer you.

Ok please answer!

Well, as far as I've seen, only your friends can see your account name, and you can set your online status just like any other game. The only other time I saw an account name shown was when I ignored someone, because ignores (Talos be praised) are account-wide.