PS didn't Columbus call the people of the Americas "Indians" as well? So pthey are indians now as they are commonly called.
Wikipedia link below is enough to clarify, however, it can make it wrongly seem that the Persians discovered and named India in 500 BCE. It is well known that ancient Indian history is a thousand years older. Hindustani Vedic caste order was likely very established by 1200 BCE [end of IVC], and the ruling Kshatriya Deva/Sharif caste whose origin was from Ur [not well known] was the top Vedic caste on the Indus.
Now about the name India or Hindustan.
en.m.wikipedia.org
"Hindush (Old Persian
cuneiform*: 𐏃𐎡𐎯𐎢𐏁, Hidūš, also transliterated as Hindūš since the nasal "n" before consonants was omitted in the Old Persian script, and simplified as
Hindūš or sometimes Hindush was
a province of the Achaemenid Empire in lower Indus Valley (modern Sindh) established after the Achaemenid conquest circa 500 BC."
[
* -
Cuneiform script originated in Ur/Sumeria. This is proof of very ancient Sumerian influence in Old Persia]
The above article says Hindus was the province of Sindh, although others say it was today's Punjab. I think it included at least Punjab, plus Sindh and maybe more.
en.m.wikipedia.org
"... some authors consider that Hindush may have been located in the Punjab area.[11]"
Note that the Hindush or the Hindus province was based on the name of Indus river, and obviously not possibly on today's Hindu people (which is a much later cultural label or identity).
The above is reaffirmed here.
en.m.wikipedia.org
"The Greek geographer
Herodotus (5th century BC) describes India, calling it ἡ Ἰνδική χώρη (Roman transliteration:
hē Hindikē chōrē, meaning "
the Indus land"), after
Hinduš, the
Old Persian name of the Indus river"
We know the Indus Land directly translates to the word Hindusthan. Logically, the inhabitants of the Land of Hindus [Hindustan] are Hindustani, which is my ancestral identity. Hindustan is also mentioned in a book of Veda.