The Gospel of Matthew says that some wise men followed a star to find Jesus, but they don't say there were three of them. The wise men brought three gifts, so it has been artistically convenient to portray them as three.
Manger scenes depict the three kings around a manger, but the wise men found Jesus in his house. In fact, they didn't find Jesus until he was one or two years old. That's why Matthew has Herod killing all the boys aged two and under, not all the newborns. Matthew was intent on inventing historical and biographical details that would confirm Jesus as like Moses and as the fulfillment of prophecy. Herod's massacre of the innocents was one such invention.
I'd like to represent the three wise men as Confucius, Lao-tzu, and the Buddha, but I don't know of a way to represent them iconically. I'd also like to invent allegorical meanings for gold, frankincense, and myrrh. Maybe they'd be love, goodness, and hope. Or, to go along with Confucius, Lao-tzu, and the Buddha, the three gifts could be wisdom, humility, and enlightenment.