The "invention" of Satan, is a very simple minded attempt to "explain" the many evils in the world. There are, have been, and always will be, tremendous evils, atrocities, and horrors, that befall humankind, and the world in general.
The animal kingdom moves on, survives, and adapts to these things. Humans have a need to explain these things. To accept such horrors, is sometimes inconceivable to most.
Satan was an attempt by mankind to "answer" why these evils happen. Its almost childlike to say that ALL evil happened, and came into this world from, and by ONE creature.
A creature that we cannot see. We cannot talk to, and we cannot ever truly know. It makes it easy to say the "boogeyman" did it. Satan is the ultimate "boogeyman". The cause for all the wrongs, but he is simply a manmade concept created to "explain" what we don't want to accept.
Yes his forms and name have changed over the years. His place in culture has changed over the years. The way in which he is used, by the clergy as a scare tactic, by the simple as an explanation, and so on and so forth.
In the end Satan is simply a name and face to place upon all that is wrong in the world.