Pi's full name is Piscine Molitor Patel. He was named after a family friend, who loved to swim and whose favorite swimming pool was the Piscine Molitor in Paris. Instead of giving their son their friend's name, Pi's parents named him after the pool! Because he is constantly teased about his name ("Pissing Patel"), he decides to shorten it simply to Pi.
I'm not great at math, but I do know that pi is a mathematical figure that represents the number 3.14. According to Math Forum (linked below), it is an irrational number because it cannot be expressed as a fraction. It is also a constant: "Pi is always the same number, no matter which circle you use to compute it." It is also an ancient number, known to the Egyptians and the Babylonians.
In changing his name, Pi goes from being a joke to being a significant "number"--maybe a little irrational, but constant as well.