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”).
The map is incorrect for Ukraine. It’s either first name + surname, or surname + first name + father’s name for the documents.
Documents always start with a surname in most countries. But traditional name order in Ukraine is as pictured, because it comes from orthodox Christians church. Same as in Greece, for example. Most people today don’t use father names anymore though.
The map shows a split between the Catholic and orthodox church with a few countries being an exception from the rule.