They are mentioned in only one of the Gospels (Matthew 2:1-12), where they are described simply as “wise men from the East.” Iran was in the East (from the perspective of Palestine) and the term “wise men” was identified with Iran’s religion of Zoroastrianism.
Matthew quotes the Wise Men as saying, “We have seen his star in the East and have come to worship him.” They followed the star to Bethlehem “till it came to rest over the place where the child was. . . . Then, opening their treasures, they offered him gifts—gold and frankincense and myrrh.”
Somewhere in time, Matthew’s unnumbered wise men became a trio and they were converted by tradition to kings as in “We three kings of orient are.” (However, to add to the confusion, an eastern tradition says there were 12 wise men—but that would make those manger scenes displayed in creches just too crowded.)
Tradition also assigned the kings different nationalities, so that only one remained Persian. However, the story in Matthew concludes by saying, “They departed for their own country”—country in the singular.
The names didn’t arrive until the Eighth Century.
Melchior, whose name means king of light, became identified as a king of Persia who brought gold, the symbol of royalty.
Gaspar or Caspar became identified as a king of India. He brought frankincense as a token of divinity.
Balthasar, whose name means Lord of the Treasures, became identified as a king of Arabia and offered myrrh in prophetic allusion to death.
The tradition of gift-giving on Christmas is supposed to have derived from the gifts the Three Wise Men brought the Christ child.
So, in a sense, what has evolved as the central non-theological theme of the season—gift-giving—is a gift from ancient Iran to the contemporary Christian world.
It isn’t the only Persian cultural tradition inserted in the Christmas holidays. The wreath was a creation that appears to have originated in ancient Parthia.