Xenya’s name day is January 24, the feast of Xenia of Petersburg.
Churches that follow the Old (Julian) Calendar keep the same feast on February 6 of the civil calendar. See everything commemorated on January 24.
The saint behind the name

Xenia of Petersburg
January 24, Holy Woman, Ξένη
Blessed Xenia of St. Petersburg lived in the eighteenth century. Widowed at twenty-six when her husband died suddenly, she gave away her possessions, put on his military coat, and took up the ascetic path of the fool-for-Christ, wandering the streets of the city for some forty-five years, praying at night in the fields and secretly helping the poor.
Also celebrating on January 24
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.