Youlianos’s name day is June 21, the feast of Julian of Tarsus.
Churches that follow the Old (Julian) Calendar keep the same feast on July 4 of the civil calendar. See everything commemorated on June 21.
The saint behind the name
Julian of Tarsus
June 21, Martyr, Ιουλιανός ο Ταρσεύς
Saint Julian was a young man of Tarsus in Cilicia, of a senatorial family, who was arrested during the persecution of Diocletian. Tradition relates that he was dragged from city to city for a year to break his resolve and finally sewn into a sack with vipers and drowned in the sea.
Also celebrating on June 21
These names share the feast, many of them other forms of the same name:
Ioulianos, Julian, Julianos, Iulian
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.