The name "Satan" means "accuser," and it's written ha-shaitan in the Old Testament. It is not a personal name, but a job title—the satan. Ha-shaitan means "the accuser" or "the adversary." Think of it as performing the office of prosecuting attorney—the one who accuses the defendant of a crime.
Now the serpent was more crafty than any other beast of the field that the Lord God had made. (Genesis 3:1)
The word translated "serpent" in this verse is nachash. It's based on an adjective that means "bright" or "brazen," like shiny brass. The noun nachash can mean "snake," but it can also mean "one who practices divination." In Hebrew, it's not uncommon for an adjective to be converted into a noun—the term is "substantivized." If that's the case here, nachash could mean "shining one," which is consistent with other descriptions of the Satan figure in the Old Testament.
For example, in Isaiah 14, the character is called "Lucifer" in the King James translation, based on the Latin words chosen by Jerome (lux + ferous, meaning "light bringer"). But the original Hebrew text actually names him—not "Light Bringer"—but Helel ben Shachar, which means "shining one, son of the dawn."