The name Benson has been derived from the Hebrew Ben-Zion (which is a historically common first and last-name in Jewish circles especially in Israel) and therefore anglicized into Benson. The word Ben in Hebrew means son! So Ben-Zion would mean Son of Zion. Another speculation would be a shortened form of Son of Benjamin or Ben's-son i.e Benson.
(Sent from: Gideon Benson)