Dosia’s name day is May 29, the feast of Theodosia of Constantinople.
Churches that follow the Old (Julian) Calendar keep the same feast on June 11 of the civil calendar. See everything commemorated on May 29.
The saint behind the name

Theodosia of Constantinople
May 29, Holy Woman, Θεοδοσία
St. Theodosia was a nun of Constantinople who suffered in the eighth century, at the outbreak of the iconoclast persecution. When the emperor commanded the destruction of the revered icon of Christ above the Chalke Gate of the palace, tradition tells that Theodosia was among the faithful who rose to defend it, and for this she was seized and put to death, sealing her love for Christ with martyrdom.
Also celebrating on May 29
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.