Sofronios’s name day is March 11, the feast of Sophronios of Jerusalem.
Churches that follow the Old (Julian) Calendar keep the same feast on March 24 of the civil calendar. See everything commemorated on March 11.
The saint behind the name

Sophronios of Jerusalem
March 11, Hierarch, Σωφρόνιος
St. Sophronios, Patriarch of Jerusalem, was born in Damascus in the sixth century. A monk and a learned theologian, he traveled the monasteries of the East with his friend John Moschos, and as patriarch he stood firm against the Monothelite heresy, defending the fullness of both the divine and human wills in Christ.
Name days: Sofronios
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.