Help - Diff between surname & farmname

Hello - I am trying to search for my family that is around the Lyngdal Norway area. My great grandfather's name is Severin Adolf Eliassen Ballestad. My grandfather made the trek from Norway to the US back in the late 1940's. He told me Ballestad was his farm name in Norway, thus he changed his last name to Syvertsen once he got to Norway. For my great grandfather listed above, what name should I search on? Also, when the family moved from one home to another, would their last name change? Thank you for your help, Nikki