Evsevios’s name day is June 22, the feast of Eusebios of Samosata.
Churches that follow the Old (Julian) Calendar keep the same feast on July 5 of the civil calendar. See everything commemorated on June 22.
The saint behind the name

Eusebios of Samosata
June 22, Hierarch, Ευσέβιος
St. Eusebios, Bishop of Samosata, was one of the great champions of the Nicene faith in the fourth century, a friend and fellow struggler of St. Basil the Great. In the years when Arianism held the empire, he traveled through the East, tradition says even in disguise, strengthening the faithful and ordaining Orthodox clergy, and for this he was driven into exile under the emperor Valens.
Also celebrating on June 22
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.