It may be this isn't asking you to think of a good brand but a sort of personality test - what sort of dog would you be? What sort of book? etc. In which case you'll just have to think of a brand you identify with: Daily Mail, righwing and terrified of everyone different? Bravo, late-night porn? Press complaints council, good at rebuking people? News Corp, ruler of the world? BBC1, stately but prone to phone-in scandals? Financial Times, global financial interests?
If in doubt, just say you're the Times.