Most old last names reflect a profession or place or are patrynomic/matrynomic. Some newer ones get very weird due to multi-culti and resulting chaos. But look at Icelandic names, they don't have much mixing and their naming system, based solely on patrynomics (sometimes matrynomics) is pretty much as it was originally conceived centuries ago.

Jon Stefansson, mean "Jon, son of Stefan" (no family name, just patrynomic). Then his son would be, for example, Eric Jonsson – Eric, son of Jon. Then his son would have the last name "Ericsson" etc… I think women use the suffix "dottir" (daughter) for their last names. Daughter of Jon = Jonsdottir.

East Slavs use the patrynomic just for the middle name and have family names. Probably because there are so many of them. There are 320 thousand people in Iceland, but 120 million in Russia alone, then also Ukraine (45 million) and Belarus (10 million), for a grand total of… a lot of east Slavs!

Give it a few decades, though. Iceland is susceptible to Western Influence, it has no army of it's own. So, in 2045 or so, Tyrone Curtisson, aka the rapper known as "Iceman" will be topping the charts in Reykjavik (now known as Da Glacier 'Hood).