Earlier quoted context omitted.
There was a stand up comedian of Algerian descent explaining that situation when the French administration tries to do the census of their colony. The custom was to use your father's and grandfather's name as a name. Problem is, many people, including brothers would have the most popular name (I think it was Mohammed). Having a Mohammed, son of Mohammed, grandson of Mohammed was common. So the French admninistration…
Having a full combination of first + family name doesn't really help for identification purposes, though: "John Smith" may not be quite as unidentifiable/ambiguous as "Mohammed, son of Mohammed, grandson of Mohammed", but it's not too far off it either. In general, websites don't depend on these names for identification; if a site refused to sign me up because I shared a name with another "Smith, John" then I would r…
A free form "full name" text could be the solution, but then the problem is forcing a formatting on it so that one person always puts the same thing in this field. Should I include second names? Accents? Is that family name first or second? At least, with clearly labeled fields you are already able to tell Adam Smith from a Smith Adam.
Webshops usually are happy with name + current address but there are administrative domains where this is not acceptable.