
The primary opposition to the name came from Native American organizations and tribal governments in the west, Midwest, and in New York State. Why is this important? Those are the Native American communities who retain more of their ancestral culture, who retain the sacredness of their traditional symbols, and who are the primary victims of racial stereotyping.
The Virginia tribes, like the Patawomeck (who I assume are most likely who you are bringing up) are very different. They are highly assimilated, having lost most of their ancestral culture and identity by the early 1900s. They began embracing it again after the 1920s primarily to escape Jim Crow segregation. They tend to be very socially conservative, and their primary priority is just having people consider them to actually be Native American. Because of this, they often embrace stereotyping.