What does the last name grotheim mean?

I don't know if the Word has a meaning, but I was told my Grotheim ancestors were from Germany or Norway & their name was originally Nelson or Nillson. When they arrived in the US they changed their name to the name of their town of origin (Grotheim) because there were too many Nillsons/Nelsons.

I hope that helps. It may be a town of origin. I am still researching my Grotheim ancestors.