When European towns got large enough that one person couldn’t possibly know everyone. Also, the Bible only has so many names, so you needed something else to differentiate the Johns and Marks and Matts.
Last names didn’t really start as names. They were descriptors you had to use because it helped people know who you were talking about, and were generally totally unofficial. For example you would refer to someone as “jeff the mason” or “jack, john’s son” or “George the Frenchman” and this is why many names you hear today are the way they are. When people started collecting written records we had to identify the 20 johns in the town, so you went by a notifying characteristic and it eventually got passed down when these traits held through generations, aka if both Jeff and his son bob are masons, you start to end up with a family title.
As democracy and republics slowly replaced morachy and kingdoms all over the world and the modern era rolled in, it became necessary for governments to know who was who, to hold a list of people in their countries, a civil register. But of course many people didn’t have last names, that was something for rich people. And you couldn’t have a million Johns in your register.
So people started picking last names, based on their nicknames, professions, etc… because they needed a last name. So if a guy named John was the smith of the village, his companions would say to the guys from the register, “oh that’s John, he’s the smith” and they would write him down as John Smith.
If John was only known as the son of Jack, then he would be John Jackson.
That’s also why some people have weird/funny names. If John fucked a dog once and was down as John the Dogfucker, he would be written down in the register as John Dogfucker.
Middle names are also important or at least middle initials. Based on my first and last name only, I was denied boarding privileges. When I added at least my middle initial, I was able to board much more easily. I also was dented credit based on my first and last name. Adding my middle name helped me wonderfully.
When we ran out of first names.