Please look at the definition of American Indian according to the federal government. https://www.law.cornell.edu/uscode/text/25/2201
According to the federal government, in order to be a Native American, one must enroll in one of the 573 federally recognized tribes, etc. An individual must connect their name to the enrolled member of a federally recognized tribe. Please see the link of the list of federally recognized tribes. The individual must have proof and follow the rules of the tribe. Each tribe has their own set of rules in becoming enrolled. For more information, please look at the links below.