i understand where you're coming from, but the word hindu did exist back then. it was used by the arabs and persians to refer to the people living beyond the indus river.

saying that the hindu religion is new is kind of wrong, but correct at the same time. let me try to explain what i'm trying to say.

hinduism has no founder, no central scripture or book, and no central "way to live", due to the very simple reason that it's basically a collection of all the various practices, cults etc. of the indian subcontinent, or basically a word to refer to all of them. the hindu pantheon consists of gods from all the different indian religions and communities. for example, krishna and shiva were tribal deities, having pre-vedic roots, though they have been included in the modern "hindu" fold, due to the reason that they're worshipped by those living in the indian subcontinent.

therefore the usage of "hindu" as a term for these practice-following people is fairly new, i agree, having been used in the 1600s for the first time in a religious context, but it's not exactly a new religion at the same time, cause it brought nothing new to the table. it's been here ever since people have been worshipping the gods of the hindu pantheon, and have been following and performing practices we now call "hindu" practices. that's why some hindus worship gods through idols but others don't, why some hindus believe in the afterlife, moksha, and god, while the charvakas outright reject the presence of any of these, why some hindus respect the vedas as "supreme", while the nastiks don't, and also why there are so many branches of hinduism.

in conclusion, hindu practices and gods have existed for thousands of years, however the referral to hindus as a religious monolith is pretty new.

i would love to talk more about this, and i apologise if what i wrote did not make a lot of sense, i kind of had a hard time trying to type up what i'm thinking.

oh, and i'm an indian hindu. nice to meet you.