In fact, the term "India" itself was derived from the Indus River!
Your question is misplaced. The South Asian name for the river is Sindhu, which was called Indus by the Greek, leading to the name India, meaning 'the country of the River Indus'. Name of the subcontinent in Hindi is Bharat.
These Western names have little to do with their religious importance in Sanatan Dharma (original name for Hinduism; the word Hindu itself is derived from the River Indus, and is a Greek creation).