How did Gertrude Bonnin get her name in the biography, The Flight of Red Bird: The Life of Zitkala-Sa?

In Woniya Kin Tinta Kin Piyawanikiye (The Breath That Brings Life to the Prairie), Tate Iyohiwin had a daughter on February 22, 1876. Tate's white husband gave the daughter the name Gertrude, but later in life, Gertrude would rename herself Zitkala-Sa, meaning Red Bird.