I probably haven’t thought this out in sufficient detail, but here goes…
How did we end up with so many last names? At least for most Europeans, everyone takes the last name of one of their parents. If that were consistently applied then there would be a fairly constant number of last names, with a lot more people with the same last name as time went on. But a look at any big city telephone book the makes me think that’s not so.
I know sometimes family lines ‘die out’ and also sometimes people change their last name when immigrating, to something more in line with local nomenclature. But I can’t say I’ve heard much about anyone just ‘inventing’ a new and unique last name.
What other things cause the number of names to grow?