Nearly everyone uses a targeting addon for arena nowadays, for example Proximo. If you name your pet after yourself, the addon will target the pet instead of you sometimes (when the pet is closer than you to the person targeting). Now this might not sound too useful, but believe me it will save your ass more than once. For example, many warlocks or mages set their poly/fear target via right clicking on proximo. You'll be surprised how many times you see your pet get randomly sheeped or feared, instead of you. Also, this is very annoying for the opposing team if they want to nuke you - as a mage I often need to sheep/CS someone and to do that I switch targets, and then continue nuking the hunter. Naming your pet like your character makes it harder to retarget you, so they have to click on you or tab-target you. Tab targeting wastes some time, especially if you drop down a snake trap or play with a shaman (targeting totems). And clicking not always works, since you can run behind a pillar or some other obstacle. It will always delay the attack for a few seconds, and those seconds can mean the difference between a loss and a win. Of course this might not help you in each arena game, but it's nice to have a little edge over the enemy.
Sorry if this has been posted before, I searched but didnt come up with anything. This might actually work with other classes, if you are making an alt or something. Some ideas include calling your shaman 'Grounding', a priest 'Shadowfiend', a mage 'Water' (what the hell :P) and so on.