Family of Elias Olsen

There was a recent post concerning my father giving a photo of Alfred Martin Telstad and a separate photo of Alma Gunarda Telstad, sister. I am a bit confused as to why the surname is Telstad not Olsen. Does this mean Elias Olsen should have been Elias Telstad and maybe he changed his name? Or is Telstad a name added to Olsen denoting an area of Norway?