'Anya' (as a given name) ultimately traces back to the name 'Anna,' which comes via Latin and Greek from the Hebrew name 'Hannah' (meaning 'favor' or 'grace'). Separately, the Hungarian word 'anya' is a native Uralic word for 'mother' (reflected in related Finno-Ugric forms).

The given name: Hebrew 'Hannah' → Greek/Latin 'Anna' → Slavic diminutive forms (e.g. Russian 'Anya') used as a familiar form of 'Anna'. The Hungarian noun: from Proto-Uralic/Proto-Finno-Ugric roots (reconstructed forms such as *äńä) evolving into modern Hungarian 'anya'.

For the personal name line: originally denoted 'favor' or 'grace' (the meaning of 'Hannah') and evolved into a widespread female personal name; the diminutive 'Anya' specifically developed as a familiar form of 'Anna'. For the Hungarian noun: the core meaning 'mother' has been stable and continues in modern usage.