Answer from a Satanist
For the most part, we feel that it was the name that was put on us.
For example, we believe in breaking all of "the 7 deadly sins" as it leads to physical, mental and emotional gratification. In previous years, the Church would have had us tortured and killed for being Devil worshippers because of the philosophies we believe in and live by.
Also, it's no secret that some Satanist perform Black masses, which again in previous years would have earned us the title (as well as an early death) of a devil worshipper, disciple of evil or a Satanist. Now that times have changed, and the Church can no longer kill us or torture us we kept up the title.
Lastly, LaVey went into some detail (which I'm not going to get into here) about how 'Satan' means the adversary. Since we oppose a lot of the Christian dogma it was a suitable title.
Satanism is, in a sense, a genre of different religions put together. Some people consider Pagans, Occultists, Wiccans, Luciferians, and Atheists to be under this category.
Answer from a Luciferian
Satanism is a very broad description. Satanism includes Luciferianism, LaVeyanism, Occultism, and several others. Satanists were considered satanists because we are considered adversaries of the Christian church.
Many LaVeyans are atheists, while all Luciferians believe in God and Lucifer (Satan). Luciferians worship Lucifer as a good deity. This is where the name came in, since Lucifer (after his fall from heaven) became Satan.
Answer from a Theistic Satanist
Our beliefs vary but we all agree that Satan is the deity we worship what differs is our belief about that deity. whichever way Satan is what we call who we worship and the reasons vary as one must get to know Satan personally.
Answer from an outsider
The name Satan simply means adversary. LaVeyan Satanists are mostly atheists and thus consider themselves adversaries to organized religion. Theistic Satanists call themselves Satanists since they worship the deity who was maligned with the name Satan and who, by nature, opposes the god of the Bible.
