Giacinto’s name day is July 3, the feast of Hyakinthos.
Churches that follow the Old (Julian) Calendar keep the same feast on July 16 of the civil calendar. See everything commemorated on July 3.
The saint behind the name

Hyakinthos
July 3, Martyr, Υάκινθος
St. Hyakinthos was a young Christian of Caesarea in Cappadocia who served at the imperial court in the time of the Emperor Trajan. When his faith became known, he refused to eat food offered to idols, and for his confession of Christ he was imprisoned and died in his bonds, still in his youth, receiving the crown of martyrdom.
Name days: Hyakinthos, Giacinto, Jacinto
Also celebrating on July 3
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.