Eugenides wrote this to a reader who asked the same question:  “the narrator of Middlesex, never refers to Chapter Eleven by his given name. Neither does anyone in the book. The nickname...is bestowed on Cal's brother by Cal himself, retroactively, in the act of writing the book....His "given name" is something I didn't give the reader.

As for the meaning of the nickname, that's another story. The character of Chapter Eleven is introduced in the first pages of the novel but it's not until page 512 that Cal provides clues as to what this name means. There's a long passage where Cal sketches what will happen to his brother in the years to come, but, unlike just about every other Stephanides family story, Cal elects not to go into it. Still, the hints are there and include the maxing out of credit cards, etc., all of which point to a situation that might involve something known in U.S. tax law as Chapter 11.

[This} is the question I get asked most often by readers of the book. The name "Chapter Eleven" really confuses people in Europe and Asia, as you might imagine. (No one files for Chapter 11 in Japan.) In some cases, Germany, for instance, where I know the language, I've worked with my translators to come up with an alternative. In the German edition of Middlesex, Chapter Eleven is called Der Pleitegeier. This refers to the circling buzzard that presages doom, usually of the financial variety.

Cal's brother is indeed referred to as "Chapter 11".  He does not have another name in the book. 

The term "Chapter 11" refers to the chapter in the United States Bankruptcy Code by which businesses can file for bankruptcy while remaining in business by submitting to reorganization of their debts under the supervision of the courts. In general conversation, the term "Chapter 11" is sometimes used as a euphemism for bankruptcy.