Hermias’s name day is May 31, the feast of Hermias the Martyr.
Churches that follow the Old (Julian) Calendar keep the same feast on June 13 of the civil calendar. See everything commemorated on May 31.
The saint behind the name

Hermias the Martyr
May 31, Martyr, Ερμείας
The Holy Martyr Hermias was an aged soldier who suffered for Christ at Comana in the second century. Summoned in his old age to sacrifice to the idols, the veteran refused, confessing the Lord whom he had served all his life, and he endured many torments with a young man's courage before being put to death by the sword.
Also celebrating on May 31
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.