the the peaks of the Everest massif are ofcourse all mountains in their own right and named according to their Tibetan/Sherpa/Chinese direction in relation to the king pin itself, Everest.

eg:
Lhotse (Lo/Lho meaning South - tse meaning peak)
Lhotse-Shar (meaning east peak on south ridge)
Nuptse (Nup meaning West)
Changtse (Chang meaning north) (also known as Bei peak - in Tibet)
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Dong Rongpu/Rongbu Shar Glacier - Rongbuk East Glacier
Xi Rongpu - Rongbuk West Glacier

Ofcourse this follows for some other himalayan massifs/mountains, otherwise peaks of a massif are named in descending order of height eg: Annapurna I, II, III, IV, followed by Gangapurna etc.

Generally, smaller mounts get the -ri suffix. eg Pumori, Gokyo Ri; or the -chuli eg Tharpu Chuli (Tent Peak).

Others might be named for their place in local culture or physical characteristics. some of the more obvious ones eg:
Kangtega (the horse saddle)
NayaKanga (new snow)
Machapuchare (fish tail)
even Roc Noir (black rock)
Kala Pattar (black rock)
Ama Dablam (mothers charmbox)
Kangchendzonga (five treasures og the great snows)

often the spelling and translation has many variations. especially in tibetan the names are often shortened.