There are still confusing exceptions: the retired footballer Eiður Guðjohnsen is not actually Gudjohn’s son; he is the son of Arnór Guðjohnsen.
Helpfully, the old Saxon custom of the eldest having a particular first name - which would be given to the next eldest if the older one inconveniently died, stuck around a good while too!
Regarding “the eldest having a particular first name which would be given to the next eldest if the older one inconveniently died”—is that referring mainly to childhood mortality? I’ve read of names being reused at times due to the (by modern standards) shocking rate of infant mortality but I’ve never heard of that particular custom.
The eldest getting a given name may have been a status thing, perhaps tied in with succession. Eldest being the one that would inherit the land or title. The young had all sorts of opportunities to die, and even escaping childhood was no guarantee as you'd then be expected to make up a Lord or King's retinue of men for any conflict. Maybe it's the origin of popes and some monarchs taking a name on succession - the "job name".
Pretty sure they go back further than that. Family names that are former patronymics (Svenson, Stevenson, Godwinson etc) are notably more common in Northern England than Southern. Reason being that was the Danelaw part of England where the Vikings held sway until roughly the Norman Conquest - 1066. They've stuck around as family names for over a thousand years.
The Domesday book was a survey of landowners and their holdings - mere peasants were listed numerically by class amongst the other holdings of the landowner, for tax and military purposes. The next attempt at a similar census was the mid 19th century. :)