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Satan is merely a fallen, not sanctified, unholy character, and is not necessarily attributed to Lucifer except for the times and periods he has been guilty and had character flaws. See illustration with the hearts. So the spirit of evil is merely the sin and evil character flaws in the current hearts and minds of every being in the Universe, both humans and angels who possess it. Both the law and spirit of evil.
Satan means "the adversary" of the highest Christ and God.
no lucifer was not his name before - it was Jerome in composing the Latin Vulgate who named him such, Isaiah 14 in the Hebrew language addresses him as Heylel (hay-lale) which means shining/hissing one son of the howling morning