I have received several emails from people whose last name is Norheim and wonder if we are related. However, since I am intimately familiar with my family genealogy I can quite definitely state that I am not related to anyone in the U.S. whose name is Norheim.
My great-grandfather was born on Nordheim farm, near Voss, Norway, and emigrated to Chicago to join his brother, whereupon he changed the spelling of his name from Nordheim to Nordhem (matching his brother's earlier change). A couple of their uncles, who had emigrated earlier to Decorah, Iowa, kept the spelling Nordheim.
Thus, the spelling of the last name that I was born with is "Nordhem". Because the "d" is not pronounced in Norsk, subsequent generations of my family in Norway have thus dropped the "d", so they are now "Norheim". After I got tired of all of the misspellings and mispronunciations of "Nordhem" that I saw and heard, I changed the spelling of my name to match my Norwegian cousins (and yes, misspellings and mispronunciations of my last name have plummeted!). All of my relatives in this country spell the name "Nordhem" or "Nordheim", none spell it "Norheim" (except my wife!).
There do seem to be quite a few Norheims around; there are quite a few families with that name across Norway and many of them had family members come to this country. Others adopted the name because they emigrated from Norheimsund in Norway. There are also some German Norheims, I believe. There is a locality called Nordheim in Wisconsin, a Nordheim church in Ransom County, North Dakota, and another Nordheim in DeWitt County, Texas. There is a locality called Norheim in Blaine County, Montana. But the only "Norheims" that I am related to are in Norway.