Mathias’s name day is August 9, the feast of Matthias the Apostle.
Churches that follow the Old (Julian) Calendar keep the same feast on August 22 of the civil calendar. See everything commemorated on August 9.
The saint behind the name

Matthias the Apostle
August 9, Apostle, Ματθίας
St. Matthias was a disciple of the Lord from the beginning, one of those who accompanied Him from the baptism of John until the Ascension. After the fall of Judas, the Apostles prayed and cast lots, and Matthias was chosen to take his place among the Twelve, as recorded in the Acts of the Apostles.
Also celebrating on August 9
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.