The profile of a Native American man, a braid trailing down and feather jutting up, is tiled into a high school hallway, dyed into the weight room carpet and laid into the turf of the football field at Salamanca city schools. School leaders say the omnipresent logo and “Warrior” name for the school athletic teams are sources of pride here, in the only U.S. city built on land leased from a Native American reservation. But as New York joins states moving to ban schools’ use of Indigenous nicknames and mascots because they diminish Native cultures, the tribe may have the...