Reminder that surnames didn't exist before the middle ages, you just had a singular name that people shouted to get your attention. Since you lived in a community of several dozen people, you didn't need to do much to differentiate yourself from the other "John" in your town because everyone knows each other. You lived and died just as "John" and would be remembered by your kids for a generation if you were lucky. There was no need to keep track of genealogy, you were a pair of hands and legs, you were supposed to get out there and plow that field and that's all your baron or lord cared about.

But somewhere after the black plague ravaged Europe and we lost a sizeable chunk of the human population, suddenly workers became in high-demand. Industrialist lords and landowners suddenly didn't have people smithing their horse shoes or making their bread, so they had to go poach people from far away towns and suddenly workers had power and options. As a way to get noticed for your family's tradeskill, you would have been wise to advertise this to wealthy employers, the best way was to attach your trade to your name. You were now John Baker to differentiate yourself from John the Drunkard if anyone came looking to hire someone who could cook bread.

So surnames are advertising. It's all it's ever been. There's nothing ancient and special about your name, it was just how your ancestors tried to make a buck.