The headword is the diminutive of ke/ntron (kappa 1338), which means "goad" (including "ox-goad"), "spear-point", "bee sting", and "point of compass", hence "centre" (LSJ s.v.).
Of the possible derived meanings, the word ke/ntrion is used in Galen to denote a surgical instrument (e.g. De compositione medicamentorum per genera, 13.407: LSJ s.v.) The meaning "ox-goad" is also claimed for the word in the Etymologicum Gudianum; the Etymologicum Magnum simply derives the word from ke/ntw and ke/ntron.
With accent shift, the word survived into Byzantine and Modern Greek as kentri/[on], "bee sting".