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Wiktionary
name day

n. The feast day of the saint after whom one is named.

WordNet
name day

n. the feast day of a saint whose name one bears

Wikipedia
Name day

A name day is a tradition in some countries in Europe and Hispanic America that consists of celebrating a day of the year that is associated with one's given name. The celebration is similar to a birthday.

The custom originated with the Christian calendar of saints: believers named after a saint would celebrate that saint's feast day, or in the Eastern Orthodox tradition, the day of a saint's death. Name days have greater resonance in the Catholic and Orthodox parts of Europe - Protestant churches showing less veneration of saints. In many countries, however, name-day celebrations no longer have connection to explicitly Christian traditions.