Bette’s name day is April 24, the feast of Elizabeth.
Churches that follow the Old (Julian) Calendar keep the same feast on May 7 of the civil calendar. See everything commemorated on April 24.
The saint behind the name

Elizabeth
April 24, Holy Woman, Ελισάβετ
St. Elizabeth was a holy woman of Constantinople who from her youth gave herself wholly to God in the monastic life. Excelling in fasting, vigil, and compassion for the poor, she became the spiritual mother of a community of nuns, and the faithful sought her prayers, through which many received healing.
Name days: Elizabeth, Elisavet, Elisa, Elise, Liza, Lisa, Beth, Bette
Also celebrating on April 24
These names share the feast, many of them other forms of the same name:
Elizabeth, Elisavet, Elisa, Elise, Liza, Lisa, Beth
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.