Longin’s name day is October 16, the feast of Longinus the Centurion.
Churches that follow the Old (Julian) Calendar keep the same feast on October 29 of the civil calendar. See everything commemorated on October 16.
The saint behind the name

Longinus the Centurion
October 16, Martyr, Λογγίνος
St. Longinus was the centurion who stood guard at the Cross of Christ and, beholding the darkness and the earthquake, confessed: truly this was the Son of God. Tradition holds that he was also among the guards at the tomb, and that having become a believer he left the army and preached Christ in his native Cappadocia.
Also celebrating on October 16
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.