The devil does not have a birthday. According to Christian tradition, the creation and fall of the angels occurred before the birth of linear time.
The devil's given name is Lucifer, which translates to "Light Bringer." Christian tradition holds that Lucifer was the most beautiful and powerful of all the angels. God made known to the angels his plan to create humankind, the fall of man, and the coming of his son Jesus Christ to redeem the human race. Lucifer balked at the idea of serving creatures he felt were beneath him. Tradition and the Book of Revelation hold that he convinced one-third of the angels to follow his rebellion against God's plan.