In Greek mythology, Kore and Persephone were interchangeable as Hades' wife. Which is it? Kore or Persephone?
As Piper notes, κόρη (kore-ay) is the Greek word for girl. The linked lexical entry lists usage as girl, bride, and daughter. All three usages are central to the Persephone myth in that, unlike her cousins, Athena and Artemis, Kore is wed.
Her myth begins in childhood, picking blossoms with her maidens, then her abduction and marriage, and finally with Demeter searching for her daughter. Demeter, literally "the Mother" in Greek (δή μήτηρ), is so bereaved, all plants die, what we now call winter.
It's not just any marriage, but marriage to the Lord of the Underworld, and not willing but by abduction--these are representative of death.
The miracle is that she returns, hearkening the rebirth of Spring. The girl has died and it is the woman, Persephone, who emerges. (Coming of Age.)
Persephone's is the cycle of death and rebirth, eventually taking the form of the Eleusinian Mysteries. (This is similar to Christ's rebirth at Easter, and the idea of the eternality of the spirit, via the Mysteries.)
In this sense, she is not just a kore, but The Kore.
- Kore is the name of the goddess as girl; Persephone as woman and queen of the netherworld.
I've read that when she was young she was called Core (maiden), and after she was kidnapped she changed her name to Persephone (bringer of destruction/death).
I see it as a sort of coming of age thing.
This is from the book (graphic novel, actually) Hades : Lord of the Dead by George O'Connor. O’Connor draws from primary documents to reconstruct and retell classic Greek myths.
It's possible that my book dramatized that a bit and she didn't necessarily choose it herself in the original myths.