With a short poem like this one, it's not likely that the poet would waste words in a title. Rita Dove makes sure to tell us an awful lot about her poem before it even starts. Here's a quick rundown:
We immediately know the main character. Persephone is kind of a weird name (sorry to all you Persephones out there). We definitely understand from the name that this is a character with a history we ought to know before we'll really understand the poem. So go do some mythological snooping, and then proceed.
We immediately know the setting. It's the part of the story when Persephone falls. It's a present moment. It's not after she fell or even right before. The whole poem is capturing one present-tense moment. It's what happened right then.
It's a double meaning. Persephone fell into the pit, sure, but she is also falling metaphorically. Falling from grace, falling from innocence, falling away from her mother's protection.
It heightens Persephone's responsibility for her downfall. Most versions of this story describe what Hades did: "The Rape of Persephone," "The Abduction of Persephone," or Ovid's "The Rape of Proserpina." (Ovid was a Roman poet, and the Romans called her Proserpina—not Persephone—just to make things more confusing.) In this version, the title makes it seem like she fell on her own, or at the very least, wasn't entirely innocent—at least according to her mama.