During British colonial rule (approximately from the 17th century until the mid-20th century), India was referred to by various names. The British East India Company, which initially arrived in India for trade purposes, began to gradually expand its influence over the Indian subcontinent.

One of the earliest references to the term "India" can be traced back to the writings of the Greek historian Herodotus in the 5th century BCE. India was known to the ancient Greeks as 'Indicus', which was derived from the Sanskrit word 'Sindhu', referring to the river Indus.

However, it was during the Mughal period that the term "Hindustan" became more widely used to refer to the Indian subcontinent. The Mughal Empire, which ruled over a significant part of the region, adopted the term "Hindustan" to denote their territory.

It was only with the arrival of the British East India Company that the term "India" began to gain prominence as the official name for the region. The British, who gradually expanded their control over India, ultimately established "India" as the official name for the country.

Despite the adoption of the term "India" by the British, the country continued to be referred to by various other names, including "Bharat" in Sanskrit and other regional languages. The Indian Constitution recognizes both "India" and "Bharat" as official names for the country.

Today, India is known by various names in different languages and cultures. The diversity of names reflects the rich history and cultural heritage of the country.