Dave, I have the same exact situation that resulted in my Flaugher Name Study. We know our immigrant ancestor, exact origin unknown, boarded the ship in Rotterdam in 1750 and the passenger list recorded his name as Christian Flaucher. He could not read or write, so all he could do was pronounce his name for the record keepers who spelled it a dozen different ways. The spelling we have now became the standard with his children's generation, but with few exceptions, the Flaugher spelling has only been found in the United States and all people by the name descend from the same man.
My goals for the study are to discover the origins of the surname, find other related lines through the help of DNA testing, search out all occurrences of the name in the United States, create and link all Flaugher profiles together on WikiTree and hopefully create the most exhaustive Flaugher resource available on the internet.
Because the name is rare, I believe these goals are achievable. For a common surname, my goals would be very different. ;-)