masc. proper name, from Latin dexter "on the right hand" (from PIE root *deks- "right, opposite of left; south"). See dexter (adj.) and compare also Benjamin.
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).