India never existed as a single sovereign country until the British took over. Before the British, India was a conglomerate of small kingdoms fighting with each other all the time. So the concept that a united India ever existed in the history is a sham. And the name Hinduism is coined by the British about 300 years ago. The words Hindu or Hinduism are not of Indian origin and they are not mentioned anywhere in any ancient Indian literature (Ramayana, Gita). A Hindu (as per Arabs and Persians) is a person living along the Indus valley, and the Moguls called the non-Muslims in India Hindus. The British followed the same tradition and finally Hindu and Hinduism become a religion.