The English term is from Greek Hindía (Ἰνδία
, via Latin India. Hindía in Byzantine (Koine Greek) ethnography denotes the region beyond the Indus (Ἰνδός
river, since Herodotus (5th century BC) ἡ Ἰνδική χώρη "Indian land", Ἰνδός "an Indian", from Avestan Hindu (referring to Sindh, and listed as a conquered territory by Darius I in the Persepolis terrace inscription). The name is derived ultimately from Sindhu, the Sanskrit name of the river, but also meaning "river" generically. Latin India is used by Lucian (2nd century).
The name India was known in Anglo-Saxon, and was used in King Alfred's translation of Orosius. In Middle English, the name was, under French influence, replaced by Ynde or Inde, which entered Early Modern English as Indie. The name India then came back to English usage from the 17th century onwards, and may be due to the influence of Latin, or Spanish or Portuguese.
Sanskrit indu "drop (of Soma)", also a term for the Moon, is unrelated, but has sometimes been erroneously connected. Listed by, among others, Colonel James Todd in his Annals of Rajputana, he describes the ancient India under control of tribes claiming descent from the Moon, or "Indu", (referring to Chandravanshi Rajputs), and their influence in Trans-Indian regions where they referred to the land as Industhan.