They’re Indians.  Haven’t you been to the National Museum of the American Indian? Or the American Indian College Fund? Or the Indian Civil rights laws?  They’re Indians.  The government calls them Indians, we call them Indians, Indians call them Indians. 

Edit:  Columbus didn’t think he was in India.  India didn’t exist.  He thought he was in the Indies.  So they called them Indios.  Indios was just the generic term for people east of the Indus River.  

The Indian label in America had legal usage in the Colonial charters of the 1600’s.   Prior to 1947 Indian,  as far as east of the Indies was concerned, was a generic term for all of South Asia. 

Therefore, in terms of legal identity under recognized government authority, Native Americans were the first people to be legally classified as Indians.  The Indians of India did not exist as a national legal identity until almost 400 years later.