That still doesn't answer why none of them asked "Kate who?"
Kate could be a nurse, a cleaner, a cook, a visitor, a patient or even a wrong number.
Culture has absolutely nothing to do with that question. Yet not once was it asked to ascertain who the caller was wanting to speak too.
Are we to believe that in India if someone rings a Hospital and asks for Sidharth that they don't ask for a surname?
Something isn't right, yet among all the angst nobody has bothered to ask "Kate who?".
You're ignoring the fact that everyone in the hospital probably knew for certain that 'Kate Middleton' was in residence and the accents used, no matter how ridiculous to most of us, may well have meant the nurse knew exactly who 'Kate' was.