Hierotheos’s name day is October 4, the feast of Hierotheus of Athens.
Churches that follow the Old (Julian) Calendar keep the same feast on October 17 of the civil calendar. See everything commemorated on October 4.
The saint behind the name

Hierotheus of Athens
October 4, Hierarch, Ιερόθεος
St. Hierotheos was an Athenian of the apostolic age, converted by the preaching of the Apostle Paul and made a bishop of Athens. Tradition remembers him as a man of deep divine wisdom, the teacher and companion of St. Dionysios the Areopagite, and relates that he was present with the apostles at the Dormition of the Theotokos, where his hymnody moved all who heard him.
Name days: Hierotheos, Ierotheos
Also celebrating on October 4
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.