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.
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.]