DIMI (Дими).  Pet form of Russian Dmitri (q.v.), meaning "of Demeter."

DIMI (דִּימִי).  Short form of Aramaic Avdimi (q.v.), meaning "destruction, loss."

... R. Dimi of Nahardea brought dry figs in a boat.  Said the Exilarch to Rabha: Go and see whether he is a scholar; then you may hold the market for him... (New Edition of the Babylonian Talmud, Rodkinson, v.5, 1902)