Listing Homebrew installed XQuartz on OS X El Capitan I installed XQuartz in OS X El Captain using the following command:

brew install Caskroom/cask/xquartz


After completion, brew list does not show XQuartz. Am I doing something wrong here?
No - you shouldn't expect to see a cask when you type brew list - instead use brew cask list to check for XQuartz and other cask-only installs.