Ariadna’s name day is September 18, the feast of Ariadne of Phrygia.
Churches that follow the Old (Julian) Calendar keep the same feast on October 1 of the civil calendar. See everything commemorated on September 18.
The saint behind the name
Ariadne of Phrygia
September 18, Holy Woman, Αριάδνη
St. Ariadne was a slave in the household of a prominent man of Prymnessos in Phrygia in the second century. When she refused to join in a pagan sacrifice for her master's son she was beaten and fled to the mountains; tradition relates that a rock opened to hide her from her pursuers and that she gave up her soul there.
Also celebrating on September 18
These names share the feast, many of them other forms of the same name:
What to say on a name day
The Greek wish is Χρόνια Πολλά (Chronia Polla), “many years.” A call or a short message on the day is what people remember. See name day wishes you can send and what a name day is.