Stauros’s name day is September 14, the feast of the Exaltation of the Holy Cross.
Churches that follow the Old (Julian) Calendar keep the same feast on September 27 of the civil calendar. See everything commemorated on September 14.
The saint behind the name

Exaltation of the Holy Cross
September 14, Great Feast, Ύψωση Τιμίου Σταυρού
The Universal Exaltation of the Precious and Life-Giving Cross commemorates the finding of the true Cross of Christ in Jerusalem by St. Helen, mother of St. Constantine the Great, in the fourth century. The Cross was raised aloft by the Patriarch before the people, who bowed down crying out for mercy. The feast also recalls the return of the Cross to Jerusalem from Persian captivity in the seventh century.
Also celebrating on September 14
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.