Peristera’s name day is January 6, the feast of Theophany.
Churches that follow the Old (Julian) Calendar keep the same feast on January 19 of the civil calendar. See everything commemorated on January 6.
The saint behind the name

Theophany
January 6, Great Feast, Θεοφάνεια
The Feast of Theophany, or Epiphany, commemorates the Baptism of our Lord Jesus Christ by St. John the Forerunner in the River Jordan. As Christ came up from the waters, the heavens opened, the Holy Spirit descended in the form of a dove, and the voice of the Father was heard — the first clear revelation of the Holy Trinity.
Name days: Theophanis, Theofanis, Phanos, Phanis, Theophanes, Fanis, Fotis, Fotios, Photios, Iordanis, Theophania, Theofania, Fani, Fotini, Foteini, Photini, Fotoula, Ourania, Rania, Theopoula, Peristera
Also celebrating on January 6
These names share the feast, many of them other forms of the same name:
Theophanis, Theofanis, Phanos, Phanis, Theophanes, Fanis, Fotis, Fotios, Photios, Iordanis, Theophania, Theofania, Fani, Fotini, Foteini, Photini, Fotoula, Ourania, Rania, Theopoula
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.