That’s interesting, because Cruz is most certainly a Spanish surname.
According to the Wikipedia entry on her, her father was White Mountain Apache and Yaqui (as was my paternal grandfather).
Many Native Americans in the Southwest have Spanish surnames which they acquired when their forefathers were baptized into the Catholic Faith under Spanish and Mexican rule. Sometimes they took Spanish names informally, such as in the case of Geronimo (which was actually “Jeronimo”, the Spanish equivalent of “Jerome”).