Stephanie’s name day is December 27, the feast of Stephen the First Martyr.
Churches that follow the Old (Julian) Calendar keep the same feast on January 9 of the civil calendar. See everything commemorated on December 27.
The saint behind the name

Stephen the First Martyr
December 27, Martyr, Στέφανος Πρωτομάρτυς
St. Stephen, the Protomartyr and Archdeacon, was one of the seven deacons chosen by the Apostles to serve the first church in Jerusalem. Full of grace and power, he preached Christ boldly; accused before the council, he beheld the heavens opened and the Son of Man at the right hand of God, and was stoned to death, praying for his slayers, while the young Saul, the future Apostle Paul, stood by.
Name days: Stefanos, Stefanis, Stephanos, Stefan, Stephen, Steve, Stefania, Stephania, Stephanie, Stefanie
Also celebrating on December 27
These names share the feast, many of them other forms of the same name:
Stefanos, Stefanis, Stephanos, Stefan, Stephen, Steve, Stefania, Stephania, Stefanie
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.