Well, it comes from the Latin translation of Isaiah 14.12, which the King James takes and translates as:
"How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations!"הילל, (heylel) which simply means "shining one." And get this: the Latin Vulgate actually uses the same word in Job 11.17: "And your life will be brighter than the noonday; its darkness will be like the morning," as well as in 2 Peter 1.19: "You will do well to pay attention to this as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts," and it even refers to Christ in Rev 22.16! "I am the root and the offspring of David, and the bright and morning star."
So we can see that unless we wanna use the term "lucifer" to describe Christ, we should probably quit using it to describe Satan. No? Actually, the ESV renders the Isaiah passage more correctly when it uses "Day Star," to translate heylel.
But the next question is, "What makes us think that Isaiah's song about the King of Babylon suddenly switches gears to talking about Satan for four verses (Is 14.12-15) and then goes back to talking about the King of Babylon? Am I the only one who finds that strange?
Strange as it may be, we actually see the same thing in Ezekiel 28. One minute our boy Zeke is talking about the Prince of Tyre, and the next moment (Eze 28.13-18) he's describing Satan. But before you write both of these instances off as grossly misinterpreted, consider that Paul called Satan an "Angel of light" in 2 Cor 11.14.
So I'd say today's myth is half true. Whatever's going on in the minds of Isaiah and Ezekiel (Double Prophecy maybe?), Paul is definitely picking up what they're puttin down. So while Satan's name is not actually "Lucifer," Scripture does teach that he's an angel of light. So be on your guard!
Sola Deo Gloria.