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

Titos
April 4, Apostle, Τίτος
St. Titus was a disciple and companion of the Apostle Paul, who called him his true son in the common faith. A Greek by birth, he accompanied Paul on his apostolic journeys, was entrusted with delicate missions to the churches, and received the epistle that bears his name, in which Paul instructs him in the ordering of the Church.
Also celebrating on April 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.