I have heard the (Nepali-speaking) Nepalis didn’t even have a name for it at that point, and I have a feeling Qomolungma wasn’t known to the Brits, because the mountain was surveyed from far away at that point.
Incidentally, “Tibetans and Nepalis on either side of the mountain”- it’s Tibetans on both sides. On the Nepali side are the Tibetan group known as Sherpa, whence we get the term Sherpa for a Nepali/Tibetan mountain guide. Further south than the Sherpa people are ‘Nepali’ people by ethnicity. (And of course properly there’s a lot more than two ethnic groups in a cross section of Nepal!)