Autonomos’s name day is September 12, the feast of Autonomous.
Churches that follow the Old (Julian) Calendar keep the same feast on September 25 of the civil calendar. See everything commemorated on September 12.
The saint behind the name

Autonomous
September 12, Hierarch, Αυτόνομος
St. Autonomos was a bishop from Italy who, during the persecution under Diocletian, came to Bithynia in Asia Minor, where he preached the Gospel and brought many pagans to faith in Christ. He was slain by a pagan mob while serving the Divine Liturgy, offering his own life together with the bloodless sacrifice.
Name days: Autonomous, Autonomos
Also celebrating on September 12
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.