Name may be modern, but Hinduism refers to Sanatan Dharm that is indigenous to India.

Let's not confuse religion with culture. By the above logic:

An average Pakistani has more in common with Hindu/Sikh Punjabi. A Bangladeshi had more in common with Hindu Bengali. Indonesian Muslims have more in common with Malay. Central Asians with watch other than Arabs, Africans with each other. Yet, there is singular Islam. Same goes for every other religion.