At a loss need suggestions please

Hello everyone, My Grandfather was Norwegian, but didn't speak Norwegian. This statement now makes sense to me as Dad recently remembered what Grandfather said he was. He was Sami, from northern coastal Norway. I can't find Grandfather in any Canadian records & I have looked at censuses & immigration. We think that perhaps the surname that we use today is not the same as would of been used in Norway. Is anyone "brave" enough to take a guess at what Kon would be shortened from. It might not even be Kon, it could be Kom as that is what is stated on his WW1 attestation papers from Canada. Thank you for any suggestions. Lisa