Not necessarily "Jonah" or "Sally" or "Tricia," although those are all very acceptable names for bags. No, I want to be able to label the bag that I keep all of my healing gear in my "Healing Gear Bag." And I want to label the bag that I keep all my quest items in "Quest Item Bag." Clear labels that help me organize exactly how things get laid out in my inventory.
Now, there's already a little bit of that going on-- "special" bags like Enchanting or Soul bags are already labeled, not to mention that you can't put anything in them that doesn't belong there. And obviously the same thing applies to quivers (Related: where on your bag bar do your hunters put your quivers? I always put mine just to the left of my backpack, but I just realized it didn't have to go there all the time).
But I want to put custom labels on all of my bags, so that if I happen to take a vacation (either out of town or to an alt), I can come back and know exactly what's where. There are lots of bag-related addons out there, and for all I know, one of them lets me do exactly this. But I'd like to see a nice and easy implementation in the normal interface.