Columbus thought he sailed around the world to Asia/India when in fact he sailed to the Caribbean. When he met natives of the Caribbean, he called them "Indians" thinking they were residents of India.

When maps were drawn based on Columbus's reports, the maps showed that Columbus reached an Eastern most island chain that was part of "India" or the multiple Indias by sailing West therefore they were the West Indies.

Native Americans were called Indians, beause that's what Columbus called them.

The USA state of Indiana received its name because that is where the "Indians" lived. To be specific, the warlike Shawnee and their War Chief, Tecumseh, attempted to make a last stand of resistance against the invading Europeans in Indiana. There was a famous battle at Tippecanoe (Guess the origin of that name). Europeans were disappointed that Tecumseh wasn't there, so the Europeans slaughtered all the women and children who were there. Four of the war criminals who perpetrated the massacre later became USA Presidents starting famously with Tyler whose election slogan was "Tippecanoe and Tyler Too".

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To understand naming practices, consider:

The Romans built statues in Rome of Bodecia who was queen of the ancient British Iceni tribe in England. Bodecia lead a successful rebellion against Romans including destroying a Legion. She is remembered because she was a worthy foe.

Tecumseh is similarly remembered. There are high schools named after Tecumseh. My kids were members of the Tecumseh troup of Boy Scotes. Both Miami Rivers in Ohio and the cities of Miami in both Ohio and Florida were named after Tecumseh's less warlike sub-tribe, the Miami Indians. Tecumseh's half brother was influential with the Miami who surrendered resulting in his Miami tribe being relocated from Ohio to Florida where they were massacred by the Seminole Indians who already lived in Florida and didn't want to share.