What does Eliana mean?
Hebrew reading parses it as El 'God' + anah 'he has answered' + a first-person yod, 'my God has answered' (per Kolatch and Alcalay). A wholly separate Latin origin also exists (Aeliana, feminine of the gens name Aelius, ultimately linked to Greek helios 'sun'); the Hebrew sense is the one carried here.
What does Anne mean?
The French and English form of Anna, ultimately from Hebrew 'Channah' (Hannah) meaning grace or favour. Long popular through St Anne, traditionally named as the mother of Mary.