Satan does not mean tempter. It means Adversary, and it is not a Christian name but a Hebrew name. It was originally a title, not a name - though it could be argued that all names, originally, were a description of a person rather than simple pretty word given to a child at birth and kept for convenience.
Satanic worship, in the scheme of things, is really quite modern. In Hebrew practice, there was little reason to be a Satanist of old because Satan was part of God's plan. Having spoken with a formerly Hasidic Jew on this topic, it was explained to me that Satan is still viewed as someone who more watches over the dead souls while they rest, as all souls are simply cleansed until they are capable of entering the realm of the divine.
This view altered with the influence of Persian belief in Zoroastrianism - near as I can tell - which painted the picture of an eternal struggle between Good and Evil, or God and Satan (or the Devil).
The name Lucifer never actually appears in any bible until it was fully mistranslated in the King James version. Prior to this, it was always "the morning star" or "the bringer of light" depending on whether you are reading it in Hebrew or Latin. Therefore, to my opinion, any bother in worshiping "Lucifer" is a misguided effort to worship a translation. But hey, worship all you want - something will be glad to take advantage.
Satanism as we see it now tends to otherwise offer Spiritual Satanists and Levayan Satanists.
Levayan practice is very frequently rooted in satire. It seeks to empower the self, but offers very little by way of worship. Even the Enochian keys offered by Levay in his ritual books are nothing more than satires based on the Enochian keys originally offered by John Dee within the Enochian magical system. The whole of this faith did not exist until the 20th century.
The Joy of Satan, and many Spiritual Satanist practices, likewise beg and borrow from other histories and faiths to create a religion that has no basis in reality or historical record. They take what they want to create an image of Satan as though he is a creator god, and the true god, and so on and so forth - and in many places lace much of it with white supremacy and other useless hate speech perfectly suitable for your average self-serving cult.
Educate yourselves before you go preaching nonsense.