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Identified errors:
This is not correct for Romania: officially it’s Surname + Given-name, live in Hungary.
Not true for Greece, it’s just First-name + Surname. It just happens that some Surnames are derived from the father’s name (think “Anderson”).
They do! Siblings both carry their father's father's name and their mother's mother's name.
Kids of siblings will not have the same family name if the siblings have different gender, but that shouldn't be an issue
Interesting! But then how do you deal with the next generation?
See my comment above:
Oh sorry, it makes sense indeed!