Why is the brother named Chapter Eleven in Middlesex?

Chapter 11 is a shorthand term for a form of bankruptcy. It's named after Chapter 11 of the US bankruptcy code and is normally used by companies in serious financial trouble who wish to be given time to restructure their debts.
In Middlesex, "Chapter 11" is the nickname given to Cal's brother by Cal himself, retroactively, in the act of writing the book. It's a sly reference to the complete mess he makes of running their father's hot dog stand franchise, Hercules Hot Dogs. Cal doesn't go into the details immediately, but by calling his brother Chapter 11, he's giving us a hint that this is someone who doesn't have much of a head for business. And so it proves, as Chapter 11 shows himself to be much more interested in the delights of self-love than in the daily grind of running a business. In that sense, he's not just a financial bankrupt but a moral one too.