How do you pronounce the names of the three wise men?

Actually, no one really knows their names. The Christmas tradition that there were three of them arose from the fact that there were three gifts (Matthew 2:11), but is without support in Scripture.

A worthless, but interesting legend of the 11th century gives their names as Gaspar (Gash'-par), Balthasar (Ball'-te-tsar), and Melchior (Mel'-key-or). The unfounded idea that they were kings is interpreted from Isaiah 60:3.