The clearest name on this page is Parvati, which means simply of the mountain — she is the daughter of Himavat, the Himalaya personified. Sanskrit parvata is a mountain, and the goddess's name is a straightforward derivation from it.
That mountain range carries another word worth noting: himālaya is hima, snow, plus ālaya, abode. And Sanskrit hima is a direct cousin of Latin hiems, winter, and Greek kheimṓn — the same inherited root, one branch using it for the season and another for the substance.
Elsewhere the naming is more local, because mountains are. Persian kūh, Arabic jabal, and the Turkic and Caucasian vocabularies each supply their own, and a great many names in this group refer to one specific mountain rather than to mountains in general — which is worth knowing before reading them as abstractions.
The qualities being wished for are consistent even where the words are not: permanence, height, shelter, and the sense of something that will not be moved.