The game is really fun, but I thought a simple and easy way to make it seem more unique for each player would be to choose different portraits for your hero.
For example. You have your basic decks that nobody really uses. Those portraits remain the same. When you create a custom deck, not only do you choose the cards that go in the deck, but now you can choose a different person. (Mages, for example, can choose either Khadgar, the late Archmage Antonidas, Rhonin, or Jaina Proudmoore; Shaman can choose Farseer Nobundo, Magatha Grimtotem, or Thrall..)
Anyway, I think it would provide even more character to your decks.