Unsurprisingly there are many different points of view.
A 1995 Census Bureau survey that asked indigenous Americans their preferences for names (the last such survey done by the bureau) found that 49 percent preferred the term Indian, 37 percent Native American, and 3.6 percent “some other name.” About 5 percent expressed no preference.
Moreover, a large number of Indians actually strongly object to the term Native American for political reasons. In his 1998 essay “I Am An American Indian, Not a Native American!”, Russell Means, a Lakota activist and a founder of the American Indian Movement (AIM), stated unequivocally, “I abhor the term ‘Native American.'” He continues…
I prefer the term American Indian because I know its origins. … As an added distinction the American Indian is the only ethnic group in the United States with the American before our ethnicity.
At an international conference of Indians from the Americas held in Geneva, Switzerland, at the United Nations in 1977 we unanimously decided we would go under the term American Indian. “We were enslaved as American Indians, we were colonized as American Indians, and we will gain our freedom as American Indians and then we can call ourselves anything we damn please.”
As with any cultural group, you will find that different people prefer different things. Personally, while I don’t feel that most people I have met use the term Native American maliciously, I do feel the term is… maybe minimizing is the right word? Hard to describe but what I mean is that there are hundreds of tribes and each is unique. The distinctive aspects and differences between the tribes are usually lost on the non native population. Anyone who knows me well knows I prefer the term Cherokee, I am a little less than half Cherokee on my fathers side. However, you just meeting me on the street, I wouldn’t expect you to know that, so Native American is fine, but try to learn a person tribe of possible. It’s usually the best option.
I prefer ‘First Nation’, ‘Native’, or ‘Indigenous’. I was born in the United States and an enrolled member of Canadian tribe, so to be called ‘Native American’ excludes the Canadian part of me (where both my parents were born). I don’t remember being referred to as ‘American Indian’ (if I were, it would be same as being called ‘Native American’).
I don’t mind ‘Indian’ although it’s the LEAST of my preference. I seems like a blah ‘name’ to me, like being called ‘Hey you female’ or ‘hey lady’, although both are true, they dont feel respectful or honoring, although I realize there might not be any disrespect from the one using it. I just prefer it LESS. Natives are honoring people’s in general.