"the Indian subcontinent, central Asia south of the Himalayas," formerly sometimes used generally for "Asia;" Old English India, Indea, from Latin India, from Greek India "region of the Indus River," later used of the region beyond it, from Indos "Indus River," also "an Indian," from Old Persian Hindu, the name for the province of Sind, from Sanskrit sindhu "river."
The more common Middle English form was Ynde or Inde, from Old French (hence Indies). The form India began to prevail again in English from 16c., perhaps under Spanish or Portuguese influence. From 1947 in reference to the Republic of India.
