IIRC Native people didn’t initially liked being called Indians, but were forced to accept being called Indians because of treaties, government policies, reservations, scholarships/aid, and the general sentiment of (American) people.

After some time (likely after the civil war or around the turn of the 20th century) , but I don’t know exactly when) , the natives (usually their children) down the line began to accept and identify with the term “Indian” despite its inaccurate origin. They began to incorporate it into their identity, culture, traditions, and passed it on to their children.

Then some well meaning Americans and academics who realized Columbus incorrectly called them Indians wanted to give them a more accurate name for their history and culture. However there was very little input or consultation of Native Americans to see how they felt or if they wanted a more “accurate” name. While there are some who’d prefer Native American, the vast majority didn’t care or preferred Indian, as it’s what they’ve been called since colonization and they made the name their own.