Etymology & Historical Origin-Kayson. Kayson is an American name invention which probably took some of its inspiration from Kasey, Karson or Kayden. As a made-up name, Kayson has no meaning (unless he’s the “son” of “Kay” or a mother with a first name starting with K).Inventing new names out of the blue is a very American naming practice.ayson-Boy Baby Name-Historic Figures. Kayson-We cannot find any historically significant people with the first name Kayson.