"Indian" is a morphing of "en Dios," the second half of what the Spanish missionaries called the continental inhabitants: "niños en Dios," meaning children in God.
"Native American" is the best among poor choices.
I would think that the best choice, though it will never catch on south of the Canadian border, is "First Nations," meaning the nations who were here first.
The "en Dios" version sounds like a later invention.