What name in the US?

On May 5 1882 Helena Maria Olsdatter b. 1848 left Oslo together with a 13 years old son; both from Ø. Toten, Oppland County. They arrived New York 1882, June 6?? on S/S Hekla. The boy was baptized JOHAN CHRISTIAN EDVARTSEN, but at the local emigrant archives and at DIGITALARKIVET the name is noted as MATHIAS EDVARTSEN (maybe a petname; I'm sure it's the same boy. What was the nAme he was registrated on in New York?? Edvartsen, Edwards, his mother patronymic changed to Olsen/Olson or something else? Is there any available records telling that? (his mother was unmarried; if she married in the US and the boy was adopted I'll have a big problem to find him..) Anyway; I'd like to trace his descendants in the US