We really don’t know their names, because the Bible doesn’t tell us. However, tradition has it that the wise men who came to honor the infant Jesus were named Gaspar, Balthasar, and Melchior.
The wise men, also known as magi, were men belonging to various educated classes. Our English word magician comes from this same root. But these wise men were not magicians in the modern sense of sleight-of-hand performers. They were of noble birth, educated, wealthy, and influential. They were philosophers, the counselors of rulers, learned in all the wisdom of the ancient East. The wise men who came seeking the Christ child were not idolaters; they were upright men of integrity.
They had apparently studied the Hebrew Scriptures and found there a clear transcript of truth. In particular, the Messianic prophecies of the Old Testament must have claimed their attention, and among these they found the words of Balaam: “A Star shall come out of Jacob; a Scepter shall rise out of Israel” (Numbers 24:17, NKJV). They certainly were acquainted with the prophecy of Micah: “But you, Bethlehem Ephrathah, though you are little among the thousands of Judah, yet out of you shall come forth to Me the One to be Ruler in Israel” (Micah 5:2, NKJV; see also Matthew 2:5, 6). They probably also knew and understood the time prophecy of Daniel regarding the appearance of the Messiah (see Daniel 9:25, 26) and came to the conclusion that His coming was near.
On the night of Christ’s birth, a mysterious light appeared in the sky which became a luminous star that persisted in the western heavens (see Matthew 2:1, 2). Impressed with its import, the wise men turned once more to the sacred scrolls. As they tried to understand the meaning of the sacred writings, they determined to go in search of the Messiah. Like Abraham, they knew not at first where they were to go, but followed as the guiding star led them on their way.
The tradition that there were three wise men arose from the fact that the Bible mentions three gifts (see Matthew 2:11), but the Bible doesn’t say how many wise men made the journey to see the baby Jesus. The unfounded idea that they were also kings came from the imagery of Isaiah 60:3.