Samson’s name day is June 27, the feast of Sampson the Hospitable.
Churches that follow the Old (Julian) Calendar keep the same feast on July 10 of the civil calendar. See everything commemorated on June 27.
The saint behind the name

Sampson the Hospitable
June 27, Venerable, Σαμψών
St. Sampson the Hospitable was a physician of noble birth who settled in Constantinople in the days of the emperor Justinian. Ordained a priest, he gave his skill and his wealth to the sick and the poor, receiving them into his own house; tradition tells that he healed the emperor himself, and with imperial help there arose the great hospice that bore his name for centuries, one of the famed houses of Christian mercy in the city.
Name days: Samson
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.