What does Bhavya mean?
From the Sanskrit भव्य (bhavya), 'grand, magnificent, splendid, noble, becoming'. A genuine classical adjective, used for both girls and (less often) boys.
What does Lavanya mean?
From Sanskrit lavanya (लावण्य), 'loveliness, grace, charm, beauty' (literally 'saltiness', extended to attractiveness). Well established.