Patapios’s name day is December 8, the feast of Patapios.
Churches that follow the Old (Julian) Calendar keep the same feast on December 21 of the civil calendar. See everything commemorated on December 8.
The saint behind the name

Patapios
December 8, Venerable, Παπάτιος
Venerable Patapios was born in Thebes of Egypt and embraced the ascetic life in the desert from his youth. Fleeing the fame that his holiness drew, he came to Constantinople, where he lived in stillness and prayer, and many were healed through his intercession; the Church's hymns remember him especially as a healer of the sick.
Also celebrating on December 8
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.