Auxentios’s name day is February 14, the feast of Auxentios.
Churches that follow the Old (Julian) Calendar keep the same feast on February 27 of the civil calendar. See everything commemorated on February 14.
The saint behind the name

Auxentios
February 14, Venerable, Αυξέντιος
St. Auxentios lived in the fifth century and served for a time at the imperial court in Constantinople before forsaking the world for the life of a hermit. He settled on a mountain in Bithynia, not far from Chalcedon, where he lived in a small cell in fasting and prayer, receiving the many who climbed to him for counsel and healing.
Name days: Auxentios
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.