In the book The Devil's Arithmetic is Hannah Chaya or is Chaya Hannah and how do you know?
In many cultures in the United States, people have two names. For example, they may have a Chinese name and then an American name. Some are changed because they are difficult for Americans to pronounce, some are changed because they want to blend in with American culture, and some are changed because there is an American equivalent. In Ireland, John is Sean. In Mexico, Antonio is Anthony. In Germany, Johann is John. In Isreal, Chaya is Hannah. Chaya is Hannah's Isreali name.
We know this because in chapter 4, she is with Schmuel and Yitzchak. They call her Chaya. She thinks,
"Chaya. but that's my Hebrew name.....The one I was given to honor Aunt Eva's dead friend. Weird." (pg 24)
So the answer to your question is that Hannah, the American, has turned into Chaya, the Isreali. They are the same person having a different experience.