Tommy’s name day is October 6, the feast of Thomas the Apostle.
Churches that follow the Old (Julian) Calendar keep the same feast on October 19 of the civil calendar. See everything commemorated on October 6.
The saint behind the name

Thomas the Apostle
October 6, Apostle, Θωμάς
St. Thomas, called the Twin, was one of the Twelve Apostles. Absent when the risen Christ first appeared to the disciples, he said he would not believe unless he touched the wounds of the Lord; eight days later Christ invited him to do so, and Thomas confessed Him as Lord and God — the clearest confession of the divinity of Christ in the Gospels.
Also celebrating on October 6
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.