Here are several suggestions:
Ingrid Washinawatok El-Issa, aka Flying Eagle Woman (1957- 1999), was a human rights activist and award-winning lecturer of Menominee descent who was kidnapped and killed by FARC guerillas in Colombia.
American Idol winner and popular country singer-songwriter Carrie Marie Underwood (born 1983) is an enrolled tribal member of the Muscogee Creek Nation (though she may not be a true Native American).
Lori Ann Piestewa (1979-2003) was the first Native American woman in American history to die in combat when she was killed in Iraq. A Hopi tribal member, Piestewa died in the attack which also wounded female soldiers Shoshana Johnson and Jessica Lynch.
A finalist for the Pulitzer Prize for Fiction (for The Plague of Doves) in 2009, Karen Louise Erdrich (born 1954) is a well known poet and novelist of Chippewan ancestry.