Thyrsos’s name day is December 14, the feast of Thyrsos and companions.
Churches that follow the Old (Julian) Calendar keep the same feast on December 27 of the civil calendar. See everything commemorated on December 14.
The saint behind the name

Thyrsos and companions
December 14, Martyr, Θύρσος
The holy martyrs Thyrsos, Leucius, and Callinicus suffered for Christ in Asia Minor in the third century, during the Roman persecutions. Refusing to offer sacrifice to the idols, they endured torments with steadfast faith and were put to death, their endurance drawing others to confess Christ.
Name days: Thyrsos
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.