The English surname, however, is literally "a dyer," attested from c. 1300, from a variant of deie "dye" (see dye (n.)) + feminine agent suffix -ster. Its immediate source is Old English degstre, from deagian "to dye." The parallel form in Middle English was deister "dyer" attested from c. 1300, from 13c. as a surname (Deyster, Dygestre).
1560s, "pertaining to or situated on the right hand," from Latin dexter "on the right hand" (source also of French dextre, Spanish diestro, Italian destro), from PIE root *deks- "right, opposite of left; south." The Latin form is with the comparative suffix -ter, thus meaning etymologically "the better direction." Middle English dester meant "right hand," and compare destrier. In heraldry, the part of the shield which is to the right when fitted on the arm, hence the side of the field to the left of the spectator.