Nothing to fancy here: the full title is The Tragedy of the Duchess of Malfi (or Dvtchesse of Malfy, if you're looking at the original 1623 title page).
Seems simple, right? And yet there's plenty of stuff to be thinking about here, though, mostly dealing with the questions of "whose tragedy is this anyway?" and "what kind of tragedy is this?"
Is this play about the Duchess herself—a nice lady with two really messed up brothers? Even if you do indeed think that this is the Duchess's tragedy, there are still more critical choices to make—you can think of this as a domestic tragedy (the main plot is, after all, about a woman, her brothers, and her husband) or as a political or social tragedy—a noble ruler is brought to destruction by social and political intrigue.
Taking another route, you could easily interpret this play as being not so much about the Duchess's personal tragedy, but rather the tragedy of a corrupt world as illustrated by her particular story.
See the difference? Instead of the tragedy of "the right noble Duchess," it's the tragedy of everybody—"Their life a general mist of error, / Their death a hideous storm of terror" (4.2.178-79), as Bosola ever so lyrically puts it.
Apart from the question of whether or not the Duchess is the tragic focus of the play, there are plenty of people who don't even think that the Duchess is the dramatic focus of the play—many critics have put together convincing cases that this play should be called The Tragedy of Bosola—to hear more about that, head on over to his "Character Analysis."