This was actually a major misunderstanding on the European's part. Europeans assumed Native Americans had a similar political structure to theirs, with a single (male) king ruling over all "his people." In reality, there wasn't really a concept of royalty among most Native Americans, and many nations were governed by councils. It is difficult to make generalizations, as differences between nations can be significant; tribes like the Navajo were extremely decentralized and, until their imprisonment at the Bosque Redondo in the 1860s, could not be said to have a single chief (and they only appointed a single person to represent the tribe then because they realized that was how to get through to the U.S. government), while tribes like the Wampanoag - you may be thinking of their sachem, Metacomet (King Philip) - did have a singular political ruler. However, consider this from the Wampanoag wiki: "The Wampanoag were organized into a confederation, where a head sachem, or political leader, presided over a number of other sachems. The English often referred to the sachem as "king," a title that misled more than it clarified, since the position of a sachem differed in many ways from that of a king. Sachems were bound to consult not only their own councilors within their tribe but also any of the "petty sachems," or people of influence, in the region. [...] Both women and men could hold the position of sachem, and women were sometimes chosen over close male relatives."

And a quick note on "Indian princesses:" they don't exist either. That is another European "creative misunderstanding," in the esteemed words of Richard White. Referring to "kings" and "princesses" helped make Natives legible to Europeans, while referring to European kings as "great fathers" helped Natives understand Europeans - at least enough to allow a healthy trade to exist. However, the "Indian princess" has a bit of a darker side to it (if you accept Vine Deloria's theory). The term, in the 19th/20th century, tends to come up in the context of a Euro-American's heritage: they are descended from an Indian Princess (usually Cherokee, for some reason). This was a defensive maneuver against the slur of having a non-white background at a time when whiteness didn't necessarily include Italians, Poles, the Irish, Catholics, Jews, and others who today are thought of as "white," and having such a non-white ancestor as a Native American was close to unthinkable. Claiming a "princess" in one's line was a way of saying that even if someone has one of...those people in their background, at least it was royalty - maybe they could even claim to have some of the better traits projected onto Natives as the noble savage. The fact that it's always a princess and never a prince or king also maintains the racial hierarchy of who's shtupping who.

I believe that calling Native headmen "king" had pretty much stopped by the time of American independence or shortly afterwards; Lewis and Clark in 1803 were explicitly looking for "chiefs" to strike deals and alliances with. However, they were pretty casual about just who they considered a chief; almost anyone willing to say he was one was considered so. This also likely involved another creative misunderstanding - while they may have negotiated with a genuine chief of one band of, say, Lakota, that negotiation would not be binding to a different band of Lakota. This was a political distinction at times lost on the Corps of Discovery; overlooking the nuances of Native politics would be a theme of 19th and 20th century U.S.-Native relationships.

Check out Richard White's The Middle Ground for an in-depth discussion about "creative misunderstandings." Other sources cited here: Vine Deloria, Custer Died for Your Sins; Phil Deloria, Playing Indian; Hampton Sides, Blood and Thunder; James P. Ronda, Lewis and Clark Among the Indians.