Members Of The Same Family Can All Have Different Last Names
Normally, in modern times, family members share their last name and it stays for generations through the father’s line, but in Iceland, they have their own last name system. Firstly, when two people get married, they keep their own last names. If they have a son, then his last name is formed by adding the suffix ‘-son’ to his father’s or mother’s first name, while a girl’s name would be formed by adding the suffix ‘-dóttir’. The suffixes literally mean ‘son’ and ‘daughter’ respectively. So that is how all of the family members can have different last names and there are no family names as we understand them now. Also, since 2019, Icelanders who identify as non-binary are allowed to add the suffix ‘-bur’ instead, which means ‘child.’
I can respect the need to control population growth. However, I am baffled by your choice to characterize the policy as "admirable in these times".