Unfortunately there is not a word for it in English. It simply does not exist in the English tradition.
So, what does the Festivity of Befana match with in the English calendar?
It is the festival of Epiphany, which stems from Greek and stands for manifestation. The Church celebrates this day as the moment when the three Wise Men (also called kings) came to visit the Holy Child in Bethlehem and when the Baby Christ was manifested to the whole world. Their names were Gaspar (India), Melchior (Persia) and Balthasar (Arabia).
This explains why the word Epiphany in English can also stand for a moment of enlightenment, of deep understanding. The Epiphany marks the end of the Christmas season and, in the past you were supposed to take down all Christmas decorations on this day.
Having said that, the Italian Befana resembles the ordinary English witch riding a broom. Yet, it is different to the witches of English descent. Operating a tight flight schedule, the Italian sibling, though old and ugly-looking, delivers gifts to children and never casts spells or any such evil things on individuals or congregations. She brings stockings with candies if you behaved in the year. If you did not, she delivers a stocking with edible sweet charcoal reminding you of your misdeeds.