Parthenius’s name day is February 7, the feast of Parthenius.
Churches that follow the Old (Julian) Calendar keep the same feast on February 20 of the civil calendar. See everything commemorated on February 7.
The saint behind the name

Parthenius
February 7, Hierarch, Παρθένιος
St. Parthenius was Bishop of Lampsakos, on the Hellespont in Asia Minor, in the fourth century, in the days of St. Constantine the Great. The son of a deacon, he was a simple fisherman in his youth, giving to the poor what he earned, and after his consecration he labored to turn his region from idolatry to Christ.
Name days: Parthenius, Parthenios
Also celebrating on February 7
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.