The words "Hindu" and "Hinduism" are described in different ways by different people. The origins and usages of the terms are not universally agreed upon. As you'll see in the references below, "Hindu" and "Hinduism" have been variously used to describe one or another of culture, geography, or religion. Some say that the terms were not used by the indigenous people until fairly recently in history, brought on by foreign peoples and governments, not their own evolution. Many say that the original collective term used for the diverse teachings of the region is "Dharma" or "Sanatana Dharma." There is some impetus in the world today to advocate these terms, either along side of, or instead of the terms "Hindu" and "Hinduism."
"The word 'Hindu' occurs nowhere in the classical scriptures of Hinduism. The ancestors of the present day Hindus did not identify themselves as Hindus."
"When Western scholars and Christian missionaries arrived on the scene, the Hindus found their faith tradition 'ism'-ized and its name became 'Hinduism'."
"That even an atheist may be called a Hindu is an example of the fact that Hinduism is far beyond a simple religious system, but actually an extremely diverse and complicated river of evolving philosophies and ancient traditions."
"The word Hindu is not a religious word. It is secular in origin. It is derived from the word Sindhu, which is the name of a major river that flows in the northwestern region of the Indian subcontinent. The ancient Greeks and Armenians used to refer the people living beyond the river Sindhu as Hindus and gradually the name stuck. When the Muslims came to the sub continent they called the people living in the region as Hindustanis to distinguish them from the foreign Muslims. Subsequently when the British established their rule, they started calling the local religions collectively under the name of Hinduism."
"Only 180 years ago Raja Ram Mohan Roy coined the word 'Hindu' to describe the huge variety of faiths and sects with similar but not identical philosophies, myths and rituals."
"[There was] no such thing as Hinduism before the British invented the holdall category in the early nineteenth century, and made India seem the home of a 'world religion' as organised and theologically coherent as Christianity and Islam. The concepts of a 'world religion' and 'religion' as we know them now, emerged during the late 18th and early 19th century, as objects of academic study, at a time of widespread secularisation in western Europe. The idea, as inspired by the Enlightenment, was to study religion as a set of beliefs, and to open it up to rational enquiry."
"According to the New Encyclopedia Britannica 20:581, 'Hinduism' was a name given in English language in the Nineteenth Century by the English people to the multiplicity of the beliefs and faiths of the people of the Indus land. The British writers in 1830 gave the word 'Hinduism' to be used as the common name for all the beliefs of the people of India excluding the Muslims and converted Christians."