As far as I can tell, there isn't a Greek name day for
Daphne. (The name does have a French name day in October.) However, there is a Greek name day in March for Laurentiou which has the same meaning as
Daphne. (Frankly, I find it a little strange because Laurentiou is a Latin-based name.)
Is is possible that your daughter could have a baptismal name with a similiar meaning while retaining her original/legal name? I did find a website that has an email address you can write to about saint names.
http://www.in2greece.com/english/saints/saints.htm