“Still, to do what they’re doing, you’re more or less selling out,” said Frank Sage, a Navajo and one of about 400 American Indian students at the university and one who says he finds the Fighting Sioux imagery hurtful and harmful. “They’re just being used.”

The lawsuit, filed last month by eight members of the Spirit Lake Tribe, is tangled, and grows out of a similarly tangled series of events that began in 2005, when the N.C.A.A. warned the University of North Dakota and 17 other colleges to change their nicknames and mascots if they wished to show the images at N.C.A.A.-controlled championships or to host such events. (Two other institutions were later added, according to the N.C.A.A.)

Since then, some colleges changed their logos, others sought and received permission from local tribes to keep them, and a few resolved the matter in other ways.

But the University of North Dakota is still at it. The state’s Board of Higher Education and the university sued the N.C.A.A. to preserve the nickname and logo, and in 2007 reached a settlement that let it keep them if the Sioux tribal councils in the state  at Spirit Lake and Standing Rock  agreed to the idea by the end of November 2010.

Image Eunice Davidson, 57, a full-blooded Sioux, is among those suing to preserve the nickname. Credit... Dan Koeck for The New York Times

But some university officials said they began worrying that the debate was leading other institutions to avoid competing against them in sports. Robert Kelley, the university’s president, has taken no position on the nickname but said he found himself being asked about it almost constantly  at the supermarket, in meetings of the state’s Congressional delegation  and wanted to ensure that the debate did not eclipse the university’s academic focus.

Politics on the reservations have also turned tense. In September, the tribal council in Spirit Lake, 100 miles west of Grand Forks, voted to allow the name. But at Standing Rock, more than 300 miles southwest of here, a past tribal chairman was deeply opposed, and a new chairman brought no clear answer, noting in a letter to state officials this fall that he would prefer an “open dialogue as opposed to a stipulated arrangement under deadline.”