Push character/monster banner to those objects

Here was a glaring case of "tell, don't ask". The idea behind tell, don't
ask is that it should not be an object's job to determine what to do
based on the state of its collaborators; instead, it should tell the
collaborators what to do, and they implement it however they want to.

We've saved a bunch of lines, and now the Player/Monsters determine
how they want to represent themselves.