The Portuguese never referred to the word hindustan. They termed their colonies in asia and africa as Portuguese Estado da Índia.

When Europe discovered native americans when they were searching for India, they didnt call them American Hindustanis. They called them American Indians.

The english term is derived from ancient Greek who spelt India as Ινδία, the first letter pronounced I not H. Iindía in Byzantine ethnography denotes the region beyond the Indus (Ἰνδός) River, since Herodotus alluded to "Indian land". Ἰνδός, Indos, "an Indian", from Avestan Hinduš refers to Sindh and is listed as a conquered territory by Persian emperor Darius I (550-486 BC) in the Persepolis terrace inscription.

This article claiming that Hindustan is a mix of Hi from Himalaya and the rest from the word indus is false.