There is the long running trope of white people claiming ancestry from a 'Cherokee Princess', which of course is in the news again due to Sen. Warren's longstanding claims and recent DNA test results (whole 'nother issue there, though). At its face, it comes off as a pretty absurd claim for so many people to have, yet I've met multiple people in the past who make it, and at its most basic, my reaction is "surely there can't have been that many Cherokee Princesses, right?" but of course looking at the claim more analytically, it raises several questions which I'm quite interested in.
First, of course, is whether the Cherokee, or other indigenous peoples of the Eastern Woodlands, had a concept of nobility and royalty that included a station actually comparable to that of 'princess' or other European ranks?
Furthermore, if so was this something that predated European contact, something that was influenced by the arriving colonial powers, or entirely a European attempt to understand system of class that was alien to them so they simply applied pre-existing titles which didn't fit all that well?
Finally, I'm also somewhat interested in the trope itself. My guess is that it originates heavily from the mythos surrounding Pocahontas, descent from whom is proudly trumpeted by the 'First Families of Virginia', but of course she was not Cherokee, so what is it about the Cherokee that attached their name to this trope so prominently?
While I may not be able to comment on the origins of the trope you refer to, I hopefully can shed some light on the accuracy of the concept of royalty in pre-Columbian cultures within Eastern North America.
Before we delve into this, we first need to figure out how we define a 'princess'. I am no expert on the origins of European nobility, but I think most people think of a prince or princess as someone related to the ruler, often a son or daughter. But what is a ruler, and what makes someone a ruler? Rulers have some authority over a region, whether it is through taxes, protection, law, or often a blend of each. I think most would agree that a ruler somehow has power over a collection of people, which is tied to the title they control in some way. Whether its the term Czar alluding to Caesar or divine kings, most rulers have some claim that makes them 'above' everyone else and therefore fit to be in charge. This can then be passed down to subsequent generations, so claiming a hereditary link to those who established a claim to rule is key. Basically, every generation of ruling class has to establish their legitimacy over everyone else. With this in mind, I am going to use the term 'princess' to mean someone who is part of some ruling class, and by their birth they were given this status in some way. Maybe they do not ever rule themselves, but they somehow posses the potential legitimacy to rule from their birth.
So do we see this in the pre-Columbian Eastern North American landscape? We definitely see a few parts that may indicate a ruling class of people in some cultures. A great example of this is the famous Mound 72 at Cahokia in western Illinois, individuals buried here have graves containing elaborate grave goods, goods that would have taken a tremendous amount of resources to obtain. In fact, throughout the Mississippian world we see exotic goods as an indicator of high social status, and on the other side we see groups interacting with Mississippians adopting aspects of Mississippian culture when they come into contact with it. This has lead some to believe that elites in Mississippian society held power by facilitating the exchange of exotic trade goods within their local areas, they drew power from their influence over other groups. Maybe they didn't physically obtain the items themselves, but they somehow had access to more than others and through this established legitimacy to be part of the upper social class. We see evidence of this influence at many sites, especially when areas first interact with what we today see as Mississippian cultures. Take Cahokia for example, prior to its rapid rise to prominence in the region the people living in the area that would become Cahokia lived in homes that were like any other in the region. But then suddenly something happened, and we see a quick (archaeologically) shift in how they lived, resulting in a complete reworking of their community. I mean that literally, they took down their homes and realigned their community to a larger axis that would be used for all structures at Cahokia. It would be like if someone came into your neighborhood, and told you and all your neighbors to tear your home down as they had a new city grid for you all to follow. Then you all do so, and suddenly everything has been rebuilt according to the new layout of your community. This would take a great deal of power to do this, people really don't like to rebuild their communities for no reason. Someone, or some group, had enough social power to make these people follow their lead. Somehow they became part of a ruling class.
So how does this all relate to your question? Native Americans prior to European arrival lived in a wide range of communities, and in the Eastern part of North America this is very true. For the most part, people lived in communities that they may have been related to and periodically would meet up with outside groups that they shared a looser relationship to. These communities would have had leadership, and often would have some sense of "us" and "them". A great example of this is effigy mounds found along the Upper Mississippi River valley, these have been argued to have served as markers for family groups in the various Coulees(valleys) along the river. This is all crucial to power structure, these markers may have been what these groups established legitimacy with, your great-great-great-great- grandfather built that mound and you use that fact to establish why you should control the resources in the vicinity. As others travel up the river, they see the many markers that show who lives in the area. You would see a effigy as an indication of some local group, and you would know that those resources were probably under their control. They held power in that very small part of the region.
Royal titles are helpful to control larger areas, and this isn't something we really see in this part of the world at this time. While we may see strong evidence to a ruling class in Mississippian communities, this is far from common and really is an outlier for the region. That's not to say that their weren't social classes in other groups, but few had the far reaching influence we see Cahokians having. Most communities probably would have been like the Effigy mounds I referred to, local communities who may have laid claims to a small portion of the region. However, most would have had some relationship to each other in their proximity, so these claims were not as binding as a ruler has over their subjects. Leaders would have been respected members of the community who may have descended from each other not because the power was linked to their birth, but simply because most of the community was related to each other.
So to sum this rambling mess up, the idea of a "Cherokee Princess" is heavily influenced by European styles of nobility and really doesn't translate well to pre-Columbian cultures in this region. The term princess requires a system of rule that is given to a lineage, your name makes you who you are. While pre-Columbian cultures had power structures, it just wasn't like what we see in Europe that led to titles like princess. You could maybe argue that local leaders could have been viewed as rulers or 'kings', but this wasn't really a title in the same sense that princess is. It would be like saying you are a prince/princess of your household, maybe you are descended from the head of your family/household, but this isn't a claim to any real sense of power as everyone in your home has some relation to each other.
I don't mean to say that all Native Americans were related or that they lived in simple societies, instead I hope I instead have made it clear that using European titles of nobility on Native American cultures is difficult. They existed in different worlds, the terms just don't have a place outside their own culture.
Boszhardt, Robert F., and Natalie Goetz. “AN APPARENT LATE WOODLAND BOUNDARY IN WESTERN WISCONSIN.” Midcontinental Journal of Archaeology, vol. 25, no. 2, 2000, pp. 269–287. JSTOR, JSTOR, www.jstor.org/stable/20708137.
https://www4.uwm.edu/archlab/cahokia/mound72.cfm
Emerson, Thomas E., and Randall E. Hughes. “De-Mything the Cahokia Catlinite Trade.” Plains Anthropologist, vol. 46, no. 176, 2001, pp. 149–161. JSTOR, JSTOR, www.jstor.org/stable/25669712.
Pauketat, Timothy R. “SPECIALIZATION, POLITICAL SYMBOLS, AND THE CRAFTY ELITE OF CAHOKIA.” Southeastern Archaeology, vol. 16, no. 1, 1997, pp. 1–15. JSTOR, JSTOR, www.jstor.org/stable/41890362.
The political structure of Pre-Columbian and early Contact era societies in the Eastern Woodlands are numerous and varied, so it'll be hard to generalize. To keep things short, I'll only talk about the two nations you mention here, the Cherokees and the Powhatans.
Among the Cherokees, there's never a social position that would equate to a "princess." What most people are really thinking of when they talk about such a thing is the daughter of the "chief" (when its not being used a euphemism for African ancestry to skirt around worse racial stigmas). And since the colonists weren't too picky about who they tossed the title "chief" unto, there were plenty of those who had plenty of daughters to go around. What the colonists called "chiefs" were several different positions within Cherokee society, including priests, councilors, and military commanders on both a local and, later, national level.
Throughout the colonial period, the Cherokee political system was constantly evolving. According to oral history, not too long before European contact, the Cherokee had overthrown a hereditary theocracy, which may represent the de-Mississippianization of Cherokee society that we see in their archaeology. The priestly families the once ruled them either became or merged into the Anigilohi clan, from which the chief priest would traditional be chosen even after the priesthood lost their exclusive hold on power.
By the early historical period, Cherokee society is governed by decentralized councils of elders collectively referred to as "Beloved Men." All men of a certain age held a seat on their local councils, but not all seats were equal. At the core of the council was still the chief priest, along with his assistant priest, the council speaker, the keeper of the council house and the council's messenger. Next came the spokesmen for each of the seven clans. These twelve men formed an inner council. The rest of the Beloved Men were arranged according to their clans and voted as bloc. Everyone else in the community could attend the council as well, and most could speak concerning the issue at hand, but only the Beloved Men would generally be involved in final deliberations.
There were also Beloved Women, women of comparable age to the Beloved Men and could also have a voice on the council. The historical record is a bit unclear whether all women of a certain age could be Beloved Women, or only those who had previous held the title of War Women by previously fighting in battle. As the Cherokee government shifted from mostly local village authority to more centralized national authority in the 1700s, women lost a lot of authority in society. This is mainly due to the increased relevance of warfare on national politics (mostly a male-oriented occupation for the Cherokee) and increased westernization which discouraged women from participating in politics. The last historic Beloved Woman was Nanyehi (also known as Nancy Ward), who died in 1822. The 1827 Cherokee Constitution officially did away with the position and completely blocked women from national government until a new Beloved Woman was appointed in 1984.
Speaking of the transition to a national government, I should probably mention the "Uku." This is the same position as what I've called the chief priest. Usually when you see references to uku, though, people are generally referring the "king" of Chota, one the main Cherokee towns. The uku of Chota is sometimes regarded as the principal chief of the entire Cherokee nation in the early historic period, but the historical record is ambiguous on this matter and it's likely that colonial writers were just aggrandizing a particularly prominent local leader. Some historic Cherokee sources, particularly Old Hop who was the First Beloved Man (head of the early national council in the mid-1750s), seem to support the idea of a singular prominent chief of this sort back in the day, but others do not. So it's still a matter of historical debate.
Now, as for the Powhatan, I can afford to be brief. We know about three ranks of nobility. These generally ranks were hereditary, unless you screwed up enough that your superior booted you from the position and gave the title to someone else. The lowest rank were the subordinate weroances who oversaw local communities. Above them were the greater weroances who oversaw regions of Tsennacommacah (as the Powhatans called their territory). Over the greater weroances was the mamanatowick, the leader of the nation as a whole. At the time of English settlement, this was Wahunsenacawh - better known today as "Chief Powhatan." Powhatan was actually the name of one of the main towns in Tsenacommacah and the place were Wahunsenacawh was born. It served as the first capital of Tsenacommacah before Wahunsenacawh moved it to Werowocomoco before the English arrived. Women could serve in any of these positions, in which case they'd be weroansquas instead. The last independent mamanatowick was Cockacoeske, a woman, who was followed by at least two more women (known to the English as Queen Betty and Queen Ann) who were subordinate to English rule.
As for Pocahontas, despite the fact that women could become weroances and mamanatowicks, she would never be her father's heir. The Powhatan society of the day was matrilineal, with inheritance following the female line. So Wahunsenacawh's heirs were his younger brothers then his nephews. The English might refer to Pocahontas as a princess because her father was a "king" or "emperor" (both ways they translated mamanatowick), but neither she nor her spouse would ever be considered to inherit the "throne" of Virginia.