I never knew her first name on Star Trek. Don’t remember anyone calling her by her first name ever.
Her first name was never used on the original series.
It didn't hurt that she was charming eye candy either.
I believe it was Jane.sc/
It was never used on TV. Some of the Star Trek tie-in novels called her Nyota, but it didn't become official until J. J. Abrams' 2009 movie.
Similarly, Sulu unofficially had the first name Hikaru before it was uttered on-screen in Star Trek VI: The Undiscovered Country.
It sounds like Ms. Nichols is going to be OK, and that's good news. My grandfather had a stroke when he was about her age, and apart from a slight speech difficulty, pulled through OK and lived for years afterwards.