Anne Pedersdatter Feiring - Surnames

Anne Pedersdatter Feiring, was according to my information on surnames really just Anne Pedersdatter. Because there were so many people with the almost same name, the folk started adding the name of the town or area they were from: hence Anne became Anne Pedersdatter på Feiring. Or as I say, Anne Pedersdatter of Feiring. Then at some point, the på got dropped. Sometimes the town or place became the middle name. Even later, the town or place became the last name or surname. I am not sure when this happened, but I believe around the 1920s. Can anyone be more exact? Or give a better explanation?