When you really think about it, William Wilson is the deepest possible name Nolan could have given CIA. You have to have an extensive knowledge of literature, English, and language in general, especially relating to names and naming in order to fully appreciate the thought put into naming the Plane Scene characters when also seeing what they go through how their personalities and their importance to the overarching narrative (that is, beyond the Plane Scene) match their names.
Just by knowing the concept behind William Wilson by Edgar Allan Poe, it can be interpreted that Bane is the double of CIA in this particular adaptation and that under the mask, Bane must look just like CIA, who is unmasked. This also means that logically the two of them have known each other a long time and have had many of the same experiences and personality. But most of all, it means that Bane's real name must be itself a variant of CIA's real name if not the exact same: William Wilson. Bane's real (first) name might be William.
This works just as much with the rest of the characters in the Scene. For example, Hugh's (who could be anyone in the Scene as he was mentioned but not given a face to match with his name) name is used in Ireland and Scotland as the Anglicized version of Aodh which comes from a word meaning "FIRE" (the fire rises), which also comes out as Aidan (Aidan Gillen, who plays CIA). Hugh also sounds like "huge" (you're a big guy).
On a side note, Slade Wilson (from the comic books, could be interpreted as CIA) has a son named Grant. Grant is derived from grand which means "great" or "large" (you're a big guy).