surname ?Leverson (Anglo) please Help

Hi My Name is Julie, My G Grandfather was from Norway. Word of mouth tells me his name was Peter Martin-Leverson. He was born about 1858 in Norway, was in NZ ,7 years before naturalised in 1887 in NZ. I believe he dropped the name leverson and became Peter Martin. We can find him untill 1918 and then he disappears from NZ. Maybe he went back to Norway to his family!!! I need help with the name Leverson. I need to know the Norwegian spelling of all of his names, and/or any help to trace his leaving Norway. Thanks