(Nobody actually cares, but I do get constant confusion as a foreigner in Budapest because people sometime expect surname-first and sometimes given-first, trying to accomodate for me)
In some situations it is less clear which convention applies. For example most of my older relatives use surname-first for their Facebook account name, which is less common with younger people. I have also seen both orders on business cards. I think most Greeks would not expect foreigners to be familiar with or follow these conventions though.
https://en.wikipedia.org/wiki/Hungarian_names
"Hungarian is one of the few national languages in Europe to use the Eastern name order, like Chinese, Japanese, Korean, Vietnamese and some Basque nationalists."
https://en.wikipedia.org/wiki/Personal_name#Eastern_name_ord...