An Indian-American friend of mine recently asked me: 

How did Indians themselves refer to India during the Raj ? Did they call it "India" ? I mean back then, it had independent state-like entities or "protectorates", with kings and other legislative bodies, as well as what are now Pakistan and Bangladesh. So how did people talk about the whole thing ? Or did they much ? How, for that matter, did the British refer to it ? And did Indians use the same words as the British did?

Today I thought of putting up here my [expanded] email response to him: 

The British referred to most of South Asia as India (recall East India Company) but the idea of "India" among South Asians arose only in the second half of British rule. I mean India as a single country or nation. Indian nationalism, a response to British rule, created that sense among the locals. Until then, allegiances and identities were mainly local (still true in some regions, though to a lesser extent in most cases). The Mutiny of 1857 was just that - a mutiny, not the First War of Indian Independence that many today like to call it (as portrayed in the atrocious movie Mangal Pandey).

That said, it is also true that most South Asians had a larger sense of being part of Hindu culture, belonging to Hindustan (with its natural geographic boundaries). Sort of like how medieval Europeans had the sense of being part of Christian culture, belonging to Christendom, even as there was a French nation and a German nation who were frequently at each others throats.

Churchill, befuddled by the diversity and the lack of sufficiently unifying criteria for a nation in India, said: "India is no more a political personality than Europe. India is a geographical term. It is no more a united nation than the Equator."

So, I'd say that in large swathes of South Asia in the Company era, there was only a loose sense of a Hindu-land/Hindustan, and lots of dominant regional identities (Marathas, Tamils, Bengalis, Gurkhas, Sindhis, Punjabis, etc.). Racially at least, the British saw them as more similar than different, and their colonial encounter eventually led to a convenient embrace of the word "Indian" by the locals (discarded later in Pakistan and Bangladesh when their Islamic identity grew dominant).

After 1947, Nehru cemented the idea of India further, as did (in no particular order) TV and the serialization of the epics, Bollywood, Pakistan, the BJP (their nationalism centered on a narrow view of Hinduism), nukes, beauty queens, IT industry, the language of middleclass consumerism, etc. Indeed, the newly resurgent nationalism and cultural pride among Indians (esp. NRIs, but also in urban middleclass India) has dramatically magnified their blindness, innocence of facts, and lack of moral self-awareness.