This is in addition to the accepted answer.
The history of the name "Lucifer" goes back to the fourth century, but it's purely about translation, never a name...
THE NAME LUCIFER HAS NEVER BELONGED TO SATAN! (Frank W. Nelte, Dec, 1995)
In 382 A.D. Pope Damasus commissioned the scholar Jerome to make an
official revision of the many Latin versions of the Bible that were
floating around in the Catholic Church at that time. Jerome went off
to a cave in Bethlehem, where he proceeded to make his translation,
the Old Testament part of which he supposedly based on the Hebrew
text. But in practice Jerome based his Old Testament very largely on
the Greek language Septuagint version (i.e. "LXX") of the Old
Testament, which Origen had produced about 140 years earlier, while in
Caesarea.
By A.D. 405 Jerome had completed his work, which we today know as "The
Latin Vulgate" Bible. It is far from a particularly accurate
translation of the original texts. Rather, it is an interpretation of
thought, put into idiomatic, graceful Latin! But "an interpretation of
thought" is only good when the translator has a perfect understanding
of "the thoughts" he is translating. But if a translator has a flawed
understanding of the thoughts he is trying to translate, then his
"interpretation of thoughts" results in a very flawed and misleading
translation.
For 1000 years this Vulgate translation was without a rival, and
herein lies the problem! The Latin Vulgate translation was the only
version of the Bible available to the people of Europe during that
period of time. There was no possibility for anyone to compare the
Vulgate with any other translation, or with Hebrew and Greek
manuscripts.
Here is a nice walk through the Latin and Hebrew...
Is "Lucifer" the Devil in Isaiah 14:12? - The KJV Argument against Modern Translations (Daniel B. Wallace)
In Isa 14:12, The KJV translators did not actually translate the Hebrew word הילל as ‘Lucifer.’ This word occurs only here in the Hebrew Old Testament. Most likely, the KJV translators were not sure what to make of it, and simply duplicated the word used in the Latin Vulgate that translated הילל. In the Vulgate, Isa 14:12 reads as follows:
quomodo cecidisti de caelo lucifer qui mane oriebaris corruisti in terram qui vulnerabas gentes.
Notice the fifth word of the text—lucifer. It is not a proper name but the Latin word for ‘morning star.’ The word lucifer occurs four times in the Vulgate: Isa 14:12, Job 11:17, Job 38:32, and 2 Peter 1:19. In Job 11:17, the KJV renders the Hebrew word בקר as ‘morning’:
et quasi meridianus fulgor consurget tibi ad vesperam et cum te consumptum putaveris orieris ut lucifer
In Job 38:32, the KJV renders the Hebrew word מזרות as Mazzaroth...
numquid producis luciferum in tempore suo et vesperum super filios terrae consurgere facis
The word means ‘constellations’ or ‘crowns’...
In 2 Peter 1:19, the KJV renders the Greek word φωσφόρος (phosphoros) as ‘day star.’ Again, the Latin Vulgate has lucifer here:
et habemus firmiorem propheticum sermonem cui bene facitis adtendentes quasi lucernae lucenti in caliginoso loco donec dies inlucescat et lucifer oriatur in cordibus vestris
In other words, lucifer is not a proper name, but is the Latin word for ‘morning star’ or ‘day star.’ The KJV simply reproduced the Latin in Isa 14:12 because they were not sure what הילל meant.
He closes with...
Since that time, Lucifer has made its way into English Bible interpretation as another name for the devil. If there is a conspiracy to sabotage the deity of Christ by translating the Hebrew word הילל in Isa 14:12 as ‘morning star,’ the same as is done with φωσφόρος in 2 Peter 1:19, then this conspiracy goes back to Jerome at the beginning of the fifth century AD! In reality, he translated the Hebrew word faithfully and the Greek word faithfully.
So, while the word "Lucifer" has made its way into Christian Bible lingo without a good basis, it does have an understandable development through history. Still, "Lucifer" is not and never was any name for any fallen angel in any text of Scrupture.