The Ballad of Lucy Whipple (2001)

When her widowed mother decides to move the family from New England to California during the Gold Rush, teenager California Morning Whipple is furious. She misses her New England home, even though her mother and younger siblings are happy in their new home and life. Not wanting anything to do with California, she renames herself Lucy. But over time "Lucy" begins to think of California as her home.