Taylor is the tailor’s name. It comes into English from Old French tailleur, “cutter”—the skilled hand who cut cloth and made clothes. After the Norman period that French trade word settled into English streets and, later, into hereditary surnames.
Like Smith and Baker, Taylor is polygenic: many separate workshops produced many separate Taylor families. Spellings Tailor and Tayler are the same idea. The name does not mean “someone who measures carefully” as a personality metaphor; it literally marked the clothing trade. When you explain Taylor at a reunion, start with scissors and cloth, not with a poetic stretch.