Tibetan vs. Nepalese vs. Chinese names

"...Tibetan name for the mountain, Chomolungma, meaning Mother of the World.
The Nepalese call it Sagarmatha or the Goddess of the Sky."

Well, I certainly don't feel that the Chinese are great spokespeople for respecting the traditions of this region, but I tend to agree that "Everest" is a johnny-come-lately name, which doesn't seem at all fitting to the region or the local cultures.

But, whose culture should be honored? Should the mountain have 2 different names, depending on whether you are approaching it from the Nepal side or the Tibet side? I'm wondering if the Sherpa people have yet another name for the mountain, or do they use the Tibetan name?