I was looking at some family history. Up until maybe the 1840s I can trace it back fine but before that they are (don't know the proper word) paternal (?) names like ben X which after the 1840s or so change to surnames which are inherited, like Goldberg (to use a stereotypical name). Why the change? Did it happen across Europe at the same time and were there very late holdouts where families still didn't use surnames like that?
Widespread adoption of surnames by Jews happened at various times in differenct places. In Italy, Jews had surnames as far back as the 10th century, since surnamces made is easier to differentiate people in large cities and when there was commerce over large distances, whereas in small towns where everyone knew each other this wasn't as neccesary. Later on this practice was adopted by Sephardi Jews in other areas.
Ashkenazi Jews got them much later, mostly as a result of laws requiring it to make taxation easier. In 1787, Emperor Joseph II of Austria-Hungary became the first leader to pass a law requiring Jews to adopt surnames. Frankfurt passed a similar law in 1807, Wesphalia in March of 1808, Napolean's France in July of 1808, Baden in 1809, Prussia in 1812, Bavaria in 1813, Posen in 1833, and Saxony in 1834. The largest requirement for Jews to adopt surnames came in 1845 when Tzar Alexander required it in the Russian Empire.