Cypriot man (Greek to me?), Giorgiou son of Georgios, for example (10)
I believe the answer is:
patronymic
'giorgiou son of georgios for example' is the definition.
(a patronymic is a name referring to one's father)
'cypriot man greek to me?' is the wordplay.
'greek to me?' indicates an anagram (something described as 'Greek to me' is confusing).
'cypriot'+'man'='cypriotman'
'cypriotman' anagrammed gives 'PATRONYMIC'.
(Other definitions for patronymic that I've seen before include "Name derived from forefather" , "Russian middle name" .)