We are from Canada, but since our culture and history are similar to the States and I have some limited personal insight, I feel I can weigh in.
My husband (and his family, of course) are First Nations. Mohawks from Tyendinaga, to be precise, so it’s not a remote location which might make a difference. They all have names that we usually describe as Western, although that term seems out of place here. Some include
Theda (grandma),
Gary (father),
Tim,
Joe,
Warren,
Bill,
Barbara,
Brenda and
Donna (uncles and aunts),
Brennan,
Melody,
Tyler,
Elliot,
Vincent,
Georgia,
Marcy,
Natasha, etc. (Cousins... there are lots more, but you get the picture.)
He went to school with a couple of people who had more traditional names, but I’m talking maybe two out of a couple hundred kids.
A few more people he knows went through the elaborate process of being granted a “longhouse name”, which is decided by the community Elders (although I’m sure you have some say) after some ceremonial stuff. He briefly looked into getting
Theodora a longhouse name, but we live about three hours from the rez so it wasn’t practical. He didn’t tell me everything it involved, just that it would take some work.
Still others simply chose a name from the Mohawk language for themselves in adolescence or adulthood. But because only about 3000 people still speak the language fluently, there have been known to be mistranslations or errors.
Even if a person has a longhouse name, or a self-endowed Mohawk name, most tend to go by their birth name for everything except Facebook, from what I’ve seen.
James sometimes calls
Theodora his ano:wara owira, which he’s pretty sure means “little/baby turtle”, but he’s not exactly fluent himself. And it’s more a term of endearment than a name.