There's no single European culture of names, patronymics or family names. Although family names are generally a late development. Not everyone with names including origins ever called themselves that; e.g. Saint Augustine of Hippo is only referred to as such to distinguish him from other saints named Augustine. Or, in cases like Leonardo da Vinci only started tacking on where he came from after he'd left there.

Here in Scandinavia, patronymics (only going back one generation) were used since as long as there's recorded history (there's no shortage of -son names in the Sagas) and faded out in the late 19th century, which is about 2-300 years after the government started keeping complete birth/death record data. There are sporadic records before that but first national-level decrees that all parishes had to keep complete records were 1608, a census was done in 1619 and the rules were extended in 1631 as conscription got important during the 30 Years War. Most people can trace their ancestries at least as far back as around 1700. Anyway, Iceland the patronymic tradition was never abandoned and people use patronymics to this day. The system endured all sorts of different governments. But adding a patronymic was not always enough to identify someone, since some names were very common. So people had nicknames, as one might expect, and those nicknames were used in official contexts - you can find them in things like court records from the middle ages up to the 19th century. That also began early; the Viking-Age king of Denmark and Norway Harald Bluetooth was not a member of the Bluetooth family; his children were not Blueteeth. He was a guy with a distinguishing dental feature.

Apparently the book you're referring to is "Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed". It does not explain Scandinavia. In fact, he does not actually support his claim that family names are a necessary condition for centralized state bureaucracy. He merely lists a few examples where name regulations were implemented (yet not always for the sake of the bureaucracy; e.g. the case of assimilating Jews) I see he mentions Iceland in a footnote (#43), so he's aware of it, yet ignores it. So Scott cherry-picks examples to support his point, even though a few examples wouldn't make for a general rule even in the best of worlds, but especially not when counterexamples are blatantly ignored.

Denmark was first, legislating in 1828 on fixed last names, although new patronymics would still occur until the 1890s. Norway's law came 1923, and Sweden in 1966. Sweden then legalized them again in 1982, Norway in 2002 and Denmark in 2006. These countries taxed everybody, conscripted everybody and so on for centuries before those dates.

However, in Sweden and Norway most people had already adopted fixed last names before the laws. Not because of the government but simply because it was what everyone else was doing in Europe. The patronymics were viewed as old-fashioned. -dotter names more than -son names as well, for which reason they disappeared faster (there are cases in the early 20th century of women adopting -son patronymics)

(I see there's a similar fallacy in the following section, blaming government for linguistic dialect levelling, although that process can and does occur by itself. People have adopted higher-[prestige](https://en.wikipedia.org/wiki/Prestige_(sociolinguistics)) dialects by themselves since always. But mass media have made it much more prominent. Most people in Sweden and Denmark do not speak in true dialect anymore. (but rather 'dialectally inflected national speech', loosely translated) Yet these countries never had any official campaign or such against dialects.

So anyway, your guy Scott doesn't cite any other studies and his own evidence is a few cherry-picked examples, completely ignoring the fact that not all of Europe adopted surnames at the same time, nor at the same point in the development of their government, and that some - which he is aware of himsefl! - did not do so at all. Just because you have a central state does not mean the entire state is concentrated to one locale. In the Scandinavian case the parish priest knows who Johan and Tomas are, and he was the lowest-tier of local representatives of the government.