Young Wizard, The answer you seek is within the Players Guide: Paying Players can see their PvP rankings in their character screen. Just press C when you are not in combat and you will see the PvP panel tab on the right.
These rankings should show up on your character sheet, on purchase requirements for some arena gear, and in the Name Tag next to your title. This pvp icon will show up during PvP combat only. When it does show up your Badge will change from the selected badge to the Ranking Name. When you leave combat it should go back to your selected badge.