Satanisms and Satanity
Just as each type or sect of Christianity is a Christism, so also do all of the various Satanisms comprise the religious complex called Satanity. The suffix '-ity' relates to the likeness of, quality of, similarity to, or fondness for a thing (in this case 'Satan' or any concept identified as 'satan').
This dovetails nicely into the commonality of all Satanisms: a positive relation to whatever is identified as 'Satan', be this symbol, cognitive, ontological in some physical sense, or something more complex than these.
As such, every Satanism individually is, literally, a singular ideology or philosophy which is endorsed or advocated and applied by the individual who associates to it.
The first known Satanism of consequence and convincement was that promoted by Anton Szandor LaVey and his group called the Church of Satan. This was expressed as a 'philosophy' in their Bible, The Satanic Bible, first published in 1969.