3 Now the serpent was more crafty than any other beast of the field that the Lord God had made.He said to the woman, “Did God actually say, ‘You shall not eat of any tree in the garden’?” 2 And the woman said to the serpent, “We may eat of the fruit of the trees in the garden, 3 but God said, ‘You shall not eat of the fruit of the tree that is in the midst of the garden, neither shall you touch it, lest you die.’” 4 But the serpent said to the woman, “You will not surely die. 5 For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil.” 6 So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate. 7 Then the eyes of both were opened, and they knew that they were naked. And they sewed fig leaves together and made themselves loincloths.
This may be a case of dramatic irony, where the audience senses something about a situation or a character (the Tempter) that another character (Eve) does not. The name of the Tempter instantly tipped off the audience that there may be something sinister about this character. "Snaky" characters have a reputation that precedes them. The connotations of the Hebrew designation are ominous.
The question is whether Eve knew the name of the Tempter. To begin with, she wasn't around when Adam named the animals. Moreover, as some commentators note (e.g. Mathews, Sailhamer), the syntax is ambiguous as to whether the Tempter even is one of the garden animals. It could be rendered that he was "subtle as none other of the beasts"–which would place him in a class apart.
Eve never addresses the Tempter by name. It's the narrator who uses that designation. So the dialogue between Eve and the Tempter resembles a movie in which viewers watch a character strap on a shaheed belt, concealed under his jacket, leave his apartment, then board a crowded subway train. It could go off at any time. Passengers are oblivious to their imminent peril.
By the same token, the narrator clues the audience into an alarming piece of information that Eve may lack. But while the audience is on the alert, Eve suspects nothing.