Google searches for "Daviana" together with either "nome" or "significato" did not give me hits on Italian pages in significant numbers. With Daviana being a frequently used Italian name this would not happen.
A rather good Italian name site,
http://www.nomix.it/, does not list the name.
Based on this I say that Daviana probably is not used in significant numbers in Italy today. Of course it could still "hide" as a rare but genuine Italian name.