Satan means "the adversary". I'll list some possible interpretations of Satan (either as a title/symbol or even as an entity). This page is work in progress so this is merely a quick draft for now.
Mythological sources:
1: The Bible
2: The Quran
3: Romantic Literature (e.g. Paradise Lost by John Milton)
4: Anton Lavey's Satanic Bible
5: others??? (I may add more)
Meanings:
1: Abrahamic concept of evil i.e. whatever goes against the ideas of Yahweh/Allah
1.1: a subset of this, for pragmatic reason, may focus more as an opposition of the violent ideas found in Christianity and Islam, or as a promotion of hedonism and indulgence (both sexual and non-sexual) with the caveat of restraining oneself from harming others.
1.2: Harming others is okay too if it allows you to reach your goals, though unlike #2 harming others should never be the goal in and of itself (Machiavellian?).
2: Secular concept of evil i.e. intentionally inflicting harm upon others (popularized by horror movies???)
3: Adversarial in the sense of stopping and sabotaging a group of people, or an ideology
4: (if my understanding is correct, etymologically deriving from Latin "adversus", though I'm not sure whether this meaning was found in the original Hebrew word "ha-Satan", "the adversary") Adversarial in the sense of "adding" new, contradictory perspectives into a belief system, though the original belief can be retained if the new one is not convincing enough. Satan in this sense can be tought as a Muse or as a teacher of knowledge. This interpretation is corroborated by both Christian and Islamic teachings, e.g. the Serpent in the Garden of Eden who added the idea of the possibility that Yahweh was lying to them when he (Yahweh) told Adam and Eve not to eat the forbidden fruit (which became an apple likely due to a calque from the Latin word "malum" which meant both "evil" and "apple"), and the idea that Satan whispers in your ears to make you doubt that Islam is the only "true" religion. In both cases it's an addition of oppositional ideas that may (or may not) make one question their previous beliefs. This will be explored further even in a psychological sense, with confirmation bias, Semmelweis reflex, anchoring effect etc. In this interpretations, Satan (when understood as an entity) can:
4.1: work on the side of the Abrahamic deity to "test" the faith of Abrahamic people (though that would necessarily imply that the Abrahamic deity is not omniscient), or
4.2: can work against the Abrahamic deity, with the goal of reducing the number of followers of Abrahamic religions: in this case, Satan's priority isn't to gain followers for himself/herself/etc. but to reduce the number of followers of Yahweh/Allah, so the existence of atheistic Satanism is perfectly coherent under this narrative.