It would appear that one can call the wise men who visited Jesus by any name one would wish, but the tradition has it they were named Gaspar, Balthasar, and Melchior.

Here is the Bible Commentary article on the wise men: Wise men, Gr. magoi, which designated men of the various educated classes. Our word "magicians" comes from this 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 the philosophers, the counselors of the realm, 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 studied the Hebrew Scriptures and there found a clearer transcript of truth. In particular, the Messianic prophecies of the Old Testament claimed their attention, and among these they found the words of Balaam: "There shall come a Star out of Jacob," (Numbers 24:17). They probably also knew and understood the time prophecy of Daniel (Daniel 9:25,26), and came to the conclusion that the Messiah's 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 Desire of Ages, page 60). Impressed with its import, the wise men turned once more to the sacred scrolls. As they sought to understand the meaning of the sacred writings, they were instructed in dreams 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 but three wise men arose from the fact that there were three gifts (Matthew 2:11), but is without support in Scripture. An interesting, but worthless, legend gives their names as...
Gaspar, Balthasar, and Melchior. The unfounded idea that they were kings was deduced from Isaiah 60:3 (cf. Revelation 21:24).

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