Iov’s name day is May 6, the feast of Job the Long-Suffering.
Churches that follow the Old (Julian) Calendar keep the same feast on May 19 of the civil calendar. See everything commemorated on May 6.
The saint behind the name

Job the Long-Suffering
May 6, Prophet, Ιώβ ο Πολύαθλος
The Righteous Job lived in the land of Uz in the age of the patriarchs, a man blameless and upright who feared God and turned away from evil. Tested by the loss of his wealth, his children, and his health, he refused to curse God, saying that the Lord gave and the Lord has taken away, blessed be the name of the Lord.
Also celebrating on May 6
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.