Iosif’s name day is December 26, the feast of King David, Joseph, James.
Churches that follow the Old (Julian) Calendar keep the same feast on January 8 of the civil calendar. See everything commemorated on December 26.
The saint behind the name
King David, Joseph, James
December 26, Saint, Δαβίδ, Ιωσήφ, Ιάκωβος
On the Sunday after the Nativity the Church keeps the synaxis of three holy kinsmen of the Lord according to the flesh: David the Prophet and King, from whose line the Messiah was born; Joseph the Betrothed, the righteous elder who guarded the Virgin and the Christ Child and led them to safety in Egypt; and James the Brother of the Lord, first Bishop of Jerusalem.
Also celebrating on December 26
These names share the feast, many of them other forms of the same name:
David, Davit, Joseph, Iossif, Josef
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.