What does Ananya mean?
From Sanskrit ananya (अनन्य), 'without another, unique, matchless'; also 'undivided' in the sense of single-minded devotion. Well established.
What does Priya mean?
From the Sanskrit priya (priyā) meaning 'beloved, dear, cherished'. A well-established Indic 'beloved' root, also the basis of Priyanka.