Sport utility vehicle icons, the Jeep Cherokee and Grand Cherokee, face a rethink for using the name of the native American tribe, which is not comfortable with the use of "Cherokee" to sell a product.

"I'm sure this comes from a place that is well-intended, but it does not honor us by having our name plastered on the side of a car," CNBC quoted Chuck Hoskin Jr., principal chief of the Cherokee Nation, as saying in a statement on Monday.

The Grand Cherokee is the brand's biggest-selling model, while the Jeep Cherokee is the company's third top-selling. Jeep is owned by Fiat Chrysler Automobile, or FCA.

Jeep recently launched a redesigned version of the Grand, and the company has sold SUVs under the Cherokee brand name for 45 years, but the Cherokee Nation believes now is the right time to put closure to this.

Hoskin says the best way to pay tribute to the Tahlequah, Oklahoma-based tribe is to learn more about its culture and history.

"The best way to honor us is to learn about our sovereign government, our role in this country, our history, culture, and language," Hoskin said in the statement quoted by CarBuzz.

Hoskin reiterated those remarks, which were first reported by Car and Driver, in an interview with CNBC on Monday.

He does not expect Jeep to immediately change the name of the SUVs, but he said the Cherokee Nation does not accept the use of the name.

Kristin Starnes, a spokesperson for Jeep's mother company, Stellantis, in a statement said that the use of the native American nation on its vehicles was carefully chosen "and nurtured over the years to honor and celebrate Native American people for their nobility, prowess and pride."

For more than four decades, Jeep has gone on the record multiple times defending its decision to use Cherokee on its SUVs. And since the reintroduction of the name to the U.S. market in 2013, the Cherokee Nation has gone on record, too, but it had never explicitly said that Jeep should change their vehicles' names.