The name Dexter looks like it is pulled exactly from Latin: the word dexter means "right, opposite of left." In ancient times and through most of human history, the right was associated with positivity, skill, and goodness. (It's no coincidence that the word "right" is both a direction and a value judgment.)
But the name has a more direct connection to Old English degstre and Middle English deister, which both mean "dyer." Like many English names and surnames, Dexter would have originally been a job designation.