[aatharuv]

India has been used in the English language for over 1,000 years, and in Latin and before that Greek for at least 1,500 years before that, along with Indian and its equivalents in other languages.

This was of course well before anyone used the word "Indian" to refer to Native Americans.

[astrange]

Even before America was discovered, "the Indies"/Indians/indios was used to refer to Ethiopia as well as India. They didn't have very clear ideas of where things were but that also suggests it was just meant to refer to any tropical area.

Or you can use backformation and say it's short for Indigenous.

[aatharuv]

The name India literally derives from the Sindhu river (aka the Indus river), which became Hindu in Persian (S->H is a common sound correspondence between Sanskrit and Persian), and dropped the initial H when getting into Greek. It was also used to refer to some areas beyond India -- (i.e, modern Indonesia or the "East Indies", but the origin of it was from civilizational India.).

I've never heard of India being used to refer to Ethiopia. Ethiopia itself is a phrase of Greek origin, and dates back at least to Herodotus.