It's derived from the Greek "soma," relating to the body I have no evidence for it, but to me, the context of 1984 suggests the latin "somnus," to sleep or dream

I think the soma drug from Brave New World (not 1984) is from sóma, a ritualistic drink / drink of the gods in Vedic literature. Huxley did indeed have an interest in Vedic mysticism according to the BNW Wikipedia article.

Soma is indeed the name of the drug used to keep the serves compliant in Brave New World.