Donald J. Trump is heading west this weekend for rallies in Las Vegas and Phoenix and a fund-raiser at Barry M. Goldwater’s old estate, known as Be-nun-i-kin, Navajo for “house on top of the hill.”

But it is the prospect of Mr. Trump’s gathering with members of the Navajo Nation that is creating the most intrigue around the trip of the presumptive Republican presidential nominee.

His repeated use of the name “Pocahontas” to deride Senator Elizabeth Warren of Massachusetts, has stirred a debate among Native Americans about how they should deal with Mr. Trump. Some Navajos are questioning whether the meeting, which is still in the works, should even take place.

For many, his mention of the historical figure is offensive and a sign that Mr. Trump, who has been accused of being anti-immigrant, also has problems with the people who first inhabited the country.