Three children were reported as belonging to a couple, but the children did not actually exist. They had apparently borrowed some neighbor children when an official had come to visit, to talk about government aid, in order to increase the amount of their subsidy. A lady prepared a very authoritative looking genealogy with good supporting documentation, but had shown some of her own children with the incorrect father. She was hiding the fact that her children had three different fathers, one of whom she had never married. I have run across surnames that are the same, but spelled multiple ways from one generation to the next, and sometimes by the same person from time to time.
People sometimes decide to sign legal documents using their nicknames.
Immigration officials often changed surnames. Some say this was done out of meanness, but I think it was more because they could not read foreign languages, and could not understand the immigrants. In my great grandmother, Sally Foy's , obituary I found an extremely frustrating inaccuracy. It had the name of her father's home town misspelled. Because of this, I could not find it for a long time.