If satanism believes all gods are just from an inventive mind then why choose "Satan" a fallen angel as you monicker?
While all gods are the inventions of the human mind, they are not equally valued inventions. Every god and every aspect of our mythology are a reflection of some cultural or social archetype. This is exactly why pantheons of gods from different cultures have a lot of overlap - because basic archetypes of the human psyche are the same. If your society wages war, there will be a god of war, or at least a god of warriors. If your society has a strong agricultural component, there will be a god responsible for growth and harvest. And so on.
Monotheistic mythology is more interesting as it represents higher-level archetypes: they are not so much about aspects of nature, as they are about aspects of human mind and the structure of society. Good and evil, order and chaos, obedience and rebellion are the archetypes were are talking about here.
Now, with the latter in mind, Satan (and equivalent figures in other mythologies - it just so happens that the Christian one is the best developed one regarding this character, which probably has to do with the fact that it has been the religion of the dominant civilization on this planet for a long time now) represents the archetypes of chaos, rebellion against authority, carnal pleasures vs "mortification of flesh", but also e.g. reason over faith, and incessant seeking and spreading of knowledge. There are various facets here which are reflected under different names - e.g. Lucifer, "light bringer", is the aspect of dabbling in and spreading "forbidden" knowledge, and those satanists who feel most strongly attached to that aspect often call themselves Luciferians.
So this really is mostly about appropriating the existing mythology with powerful symbols that people can readily understand and connect to. This is done with full understanding and acknowledgement that it is mythology; it doesn't really matter, because it's about getting the point across, and you need emotional symbolism here as much as rational argument for full effect.