Meaning of Kyson. English name. In English, the name Kyson means-son of kyle.The name Kyson originated as an English name. The name Kyson is most often used as a boy name or male name.English Name Meaning-son of kyle. Origin-England.nglish name. In English, the name Kyson means-son of kyle.The name Kyson originated as an English name. The name Kyson is most often used as a boy name or male name. English Name Meaning-son of kyle. Origin-England.