The formal Hebrew name of the holiday is Yom HaKippurim, 'day of the atonement'. This name is used in the Bible, Mishnah, and Shulchan Aruch. The word kippurim 'atonement' is one of many Biblical Hebrew words which, while using a grammatical plural form, refers to a singular abstract concept.
Beginning in the classical period, the singular form kippur began to be used in piyyut, for example in Unetanneh Tokef, alongside the standard plural form kippurim. Use of kippur spread In the medieval period, with Yom Kippur becoming the holiday's name in Yiddish and Kippur in Ladino. In modern Hebrew, Yom Kippur or simply Kippur is the common name, while Yom HaKippurim is used in formal writing.
In older English texts, the translation "Day of Atonement" is often used.