Black Beauty is a remarkably straightforward book—there aren't a lot of hidden messages here. Anna Sewell wants to be sure we really understand her messages about animal cruelty, so she doesn't conceal much with metaphor or allegory.
One type of symbolism Sewell does bust out, though, is in her characters' names. She often gives them very literal names to show that they might stand for an idea or type of person. A thieving groom is called "Filcher," an inexperienced one is given the last name "Green," and a kind farmer's surname is "Thoroughgood"—all clues that these people aren't really fleshed-out characters, but general types of people who play different roles in a horse's life.