Well said. Almost right after Kirk and "Harrison" meet face to face, Khan says his true name. He is not hiding it at all. Its Admiral Marcus who is. I do not think it would have changed the drama to have it revealed in the promotion.
They are naive to think this was ever a real secret. All the secrecy alone was a huge sign that the reveal would mean something to most viewers and not just fans. Anyone other than Khan would not have been known to most people. So "hiding" it was a huge tell itself.