Pen names?
Not sure how Chicago manual of style handles pen names. I was including "Curiosa mathematica, V2" which was really authored by Lewis Carroll. However the pen name on the book is "Charles Lutwidge Dodgson". Sort of weird problem.
This is an old discussion that has not been active in a long time. Before commenting here, you should strongly consider starting a new discussion instead. If you think the content of this discussion is still relevant, you can link to it from your new discussion.
CMoS suggests that, when the real name is known, you _can_ (if it is of interest to the reader) add it in square brackets after the pseudonym. Typically you'd e.g. not add [Samuel Clemens] to a Mark Twain book.
That said, you're dealing with the opposite case here - Dodgson was his real name, Lewis Carroll was the pen name. I'd still follow the same practice, though, i.e. cite as CL Dodgson [Lewis Carroll, pseud.]