Like it or not, from experience of visiting elderly relatives in hospital, I don't believe I'd be asked what name I'd prefer to be called in that situation. Or maybe, in such a vulnerable position, I'd be unable to make my preference clear. In that case, I'd hope the medical staff would consult my adult children. I think the default should be Mrs Popbottle until my wishes are clarified. I've been known by that name since 1975, when I married Mr Popbottle so I would certainly respond to that name.
My reasoning is this: My father-in-law was christened Henry but his friends and family called him Harry. He never used the name Henry. Other people called him Mr Popbottle. In hospital, the name written on the whiteboard above his bed was Henry. The patronising, baby voices would say, "Come along, Henry, it's time for your medication." or " Here's your cup of tea, Henry." How demeaning!
Worse than that, my mother-in-law was christened Mary Lilian but always went by Lilian, Lil (only by her husband) or of course, Mrs Popbottle. In hospital, the name above the bed was Mary. And the patronising voices used that name.
Both these people lived through and served in the armed forces during WWII. Harry was never out of work. Both deserved the respect of being addressed by their formal name Mr or Mrs Popbottle. No one asked me or my sons or daughter if the name on the whiteboard was right. The first name on their medical records would have been their surname. Much less chance of giving offence if that name had been used.