Son of Harry
A patronymic surname of English origin meaning 'son of Harry'. While Harry is a medieval diminutive of Henry, Harison is a rare spelling variant of the more common Harrison.
Less common today
Harison isn't in the latest US Top 1000. It last peaked at #9,119 in 1990.
US births per 5-year period, 1990βpresent (SSA data).