Christian’s name day is December 25, the feast of the Nativity of Christ.
Churches that follow the Old (Julian) Calendar keep the same feast on January 7 of the civil calendar. See everything commemorated on December 25.
The saint behind the name

Nativity of Christ
December 25, Great Feast, Χριστούγεννα
The Nativity of our Lord and God and Saviour Jesus Christ, kept on December 25, celebrates the birth in the flesh of the Son of God from the Virgin Mary in Bethlehem. Laid in a manger because there was no room at the inn, the newborn King was glorified by angels, worshipped by shepherds, and honored with gifts by Magi from the East.
Name days: Christos, Christodoulos, Chris, Christian, Christoforos, Hristos, Emanuel, Emmanuel, Christopher, Christakis, Christiana, Christina, Christine, Kristina
Also celebrating on December 25
These names share the feast, many of them other forms of the same name:
Christos, Christodoulos, Chris, Christoforos, Hristos, Emanuel, Emmanuel, Christopher, Christakis, Christiana, Christina, Christine, Kristina
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.