What does Prisha mean?
A modern name usually traced to Sanskrit for 'beloved, dear'. It is also widely glossed 'God's gift' and linked to Lakshmi, but that reading is popular rather than documented and its Sanskrit basis is unsettled (an Arabic 'gift' root is also cited).
What does Ananya mean?
From Sanskrit ananya (अनन्य), 'without another, unique, matchless'; also 'undivided' in the sense of single-minded devotion. Well established.