That's pretty cool.
You mean to say that they only had one name? Kinda like Cher, Sting, and Madonna? That must have gotten folks mixed up unless the population was really small.
Do the Sioux tend to follow the religions of their namesakes? Do ones with scandinavian last names tend to be Lutheran or french surnames catholic? (I'm not trying to be funny; the question is legit.)
Generally yes they had single word or phrase names like Bigfoot, Sitting Bull, Black Cat, and Wolf Guts. Many of these names later became the last names of their descendants. I don't think there were too many mix ups as names were unique and native populations were small. Also folks did not live as long as they do todays making the likelihood of mix ups rather low.
The religious practices of the Sioux by and large have nothing to do with names. You must remember that many of the French names for instance date from the days of the fur trade. French fur traders were commercially oriented frontiersman and were not all that religious. Later on (after the reservations had been established) the religions practiced depended upon who they had intermarried with and other cultural influences (just like today).