Sanatana Dharma originated in India. India also has another name: "Bharata/Bharathavarsha". The term ArshaBharata culture is commonly used for pointing out the Sanatana Dharma in South India. How did the nation get this name?
After the name of an ancient king Bharata, India is also known as Bharata-varṣa since the prehistoric times. Before it, this land was called as Ajanābha-varṣa. This is stated in Shrimad Bhagavatam:
ajanābhaṁ nāmaitad varṣaṁ bhāratam iti yata ārabhya vyapadiśanti. [SB - 5.7.3]
The name of this land was Ajanabha. It came to be known as Bharata after starting of his (King Bharata) reign.