It's complicated. Lucifer as the "proper name" for the Devil is something that happened very late. The word
lucifer only appears four times in the Vulgate (Latin Bible) and is never used as a reference to the Devil. In Latin the word
lucifer refers to the morning star, which in Greek is
eos and in Aramaic is
helel. Initially, references to
lucifer weren't considered references to the Devil. But eventually Lucifer became just another assumed name for the Devil, like Satan, Beelzebub, Belial, Hades, etc.
During the later Middle Ages and Enlightenment it was popular among theologians, witch experts and writers on the occult to classify and category demons and angels, as there was a general need for categorization. There were tons of grimoires and occult texts, as well as the books on the Kabbalah, whose authorship was often ascribed to famous writers, theologians or occult figures like Kabbalistic writers, which tried to categorize and summarize the various demons, angels, etc., which were popular among a lot of people. You have to keep in mind that people didn't have the internet, and source criticism was generally not a thing. Nor did people have casual access to Rome or learned scholars who could speak authoritatively on Biblical or theological matters.
The Lucifer name eventually started sticking as the proper name for the Devil post-Middle Ages, partly because of the popularity of the King James version, which is one of the Bible versions that stressed the association between the word Lucifer and the Devil. A movement that only accepts the King James version and rejects all later translations was popular especially amongst US Baptists. Both Luther and Calvin basically said people were idiots for thinking Lucifer referred to the Devil, but it's evident people generally didn't care.
I suggest you read up on the history of the word Lucifer and the classification of demons if you're interested, as I doubt I can explain everything properly. The Wikipedia articles for
Lucifer and
the classification of demons are a good place to start. If you've played Shin Megami Tensei or Persona or some other games and wondered why Satan, Lucifer, Beelzebub, etc. are different beings, all this shit is why.
