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Heh, it's funny, I've never thought about it. :) It derives from Greek "stoma" (stomatos), which means "a mouth"), it's your bad luck that stomach means "желудок" in English. :)

But you do have an...

национальность - In Russian it means ethnicity, in English nationality means what country you are a citizen of (гражданство in Russian).

That's a very useful link -- thanks!

I came across one that's very much a false cognate:

РЕАБИЛИТАЦИЯ
1. Восстановление в юридических правах.
2. перен. Восстановление доброго имени, прежней...