It has cultural significance and leaks information. People sharing the same "family name" are presumed to be family. Patronymics show in which way people are re

It has cultural significance and leaks information. People sharing the same "family name" are presumed to be family. Patronymics show in which way people are related (whether or not certain two people are father and child). Some names in some countries also leak gender and sometimes also martial status. Spliting the name into "given name" and "family" name allows people to change family name to signal significant changes (e.g. marriage) happened. You could of course say it's irrelevant and should not happen, but it's fun and people like this kind of fun. You could of course go full Myanmar and say "put whatever here and also it's about 70 bucks fee to change it whenever you want to whatever you want", but that opens a host of other administrative problems, as global demographic database luckily is not a thing.