In Mexico the name is not the epiphany instead it is called Day of the Holy King.
On this day the celebrate the three magi that went to meet Jesus right after he was born.
On this day you can receive gifts.
Some kids will write letters to the three magi and they would place the letter in a helium filled ballon and release them.
That is Rosca de Reyes. It is a sweet bread shaped like a wreath, with candied fruit on top, and a baby Jesus figure is baked inside. The person who get the baby Jesus in their piece has to host Día de la Candelria on February 2nd.
They believe the names of the three kings are Melchor, Gasper, and Baltazar.
On January 5th, they will add the magi to the nativity scene.