Yes, "Bharat" (the first 'a' pronounced as in 'car' while the second 'a' pronounced as in 'cut') is another name for India... It is the actual Hindi/Sanskrit name for the country. "Hindustan" is another name, derived from Urdu, I think, and 'India' is an anglicized version of its root 'Hind' (the 'i' pronounced as in 'pin'). The name "Bharat" was given after a famous ancient king "Bharat" (both 'a's pronounced as in 'cut,') whose story has contributed richly to the Indian mythology.