Origin of the name Bharata or Bharata-varṣa (Bharat)

The name Bhārata or Bhārata-varṣa (Bharata-varsha) is said to be derived from the name of either Dushyanta’s son Bharata or Rishabha’s son Bharata.
Several Puranas state that it is derived from the name of Bharata, the son of Rishabha. However, some Puranic passages state that it is derived from Bharata, which was another name for Rishabha’s ancestor Manu . Some other Puranic passages refer to the Bharata people, who are described as the descendants of Dushyanta’s son Bharata in the Mahabharata.
The earliest recorded use of Bhāratavarṣa in a geographical sense is in the Hathigumpha inscription of King Kharavela (first century BCE), where it applies only to a restrained area of northern India, namely the part of the
Gangetic Valley west of Magadha. In the Sanskrit epic, the Mahabharata (200 BCE to 300 CE), a larger region of North India is encompassed by the term, but much of the Deccan and South India are still excluded.
Bhārata has been used as a self-ascribed name by some people of the Indian subcontinent and the Republic of India.
The designation Bhārata appears in the official Sanskrit name of the country, Bhārata Gaṇarājya . The name is derived from the ancient Hindu Puranas , which refer to the land that comprises India as Bhāratavarṣa (Sanskrit: भारतवर्ष, lit. country of Bharata ) and uses this term to distinguish it from other varṣas or continents. For example, the
Vayu Purana says ” he who conquers the whole of Bhāratavarṣa is celebrated as a samrāt (Vayu Purana 45, 86).”
The Sanskrit word bhārata is a vṛddhi derivation of Bharata , which was originally an epithet of Agni. The term is a verbal noun of the Sanskrit root bhr-, “to bear/to carry”, with a literal meaning of to be maintained (of fire ). The root bhr is cognate with the English verb to bear and Latin ferō . This term also means “one who is engaged in search for knowledge”. Barato , the Esperanto name for India, is also a derivation of Bhārata
According to the Puranas, this country is known as Bharatavarsha after Bharata, the son of Rishabha . This has been mentioned in Vishnu Purana (2,1,31), Vayu Purana (33,52), Linga Purana (1,47,23), Brahmanda Purana (14,5,62), Agni Purana (107,11–12), Skanda Purana, Khanda (37,57) and Markandaya Purana (50,41), all using the designation
Bharata Varsha .
Vishnu Purāna mentions:
ऋषभो मरुदेव्याश्च ऋषभात भरतो भवेत्
भरताद भारतं वर्षं, भरतात सुमतिस्त्वभूत्
Rishabha was born to Marudevi , Bharata was born to Rishabha,
Bharatavarsha (India) arose from Bharata and Sumati arose from Bharata.
—Vishnu Purana (2,1,31)
ततश्च भारतं वर्षमेतल्लोकेषुगीयते
भरताय यत: पित्रा दत्तं प्रतिष्ठिता वनम (विष्णु पुराण, २,१,३२)
This country is known as Bharatavarsha since the times the father entrusted the kingdom to the son Bharata and he himself went to the forest for ascetic practices.
—Vishnu Purana (2,1,32)
uttaraṃ yatsamudrasya himādreścaiva dakṣiṇam
varṣaṃ tadbhārataṃ nāma bhāratī yatra santatiḥ
उत्तरं यत्समुद्रस्य हिमाद्रेश्चैव दक्षिणम् ।
वर्षं तद् भारतं नाम भारती यत्र संततिः ।।
“The country (varṣam ) that lies north of the
ocean and south of the snowy mountains is called Bhāratam ; there dwell the descendants of Bharata.”
—Vishnu Purana
The Srimad Bhagavat Purana mentions(Canto 5, Chapter 4) – “He (Rishabha ) begot a hundred sons that were exactly like him… He (Bharata) had the best qualities and it was because of him that this land by the people is called Bhârata-varsha”
The Bhāratas were also a Vedic tribe mentioned in the Rigveda , notably participating in the Battle of the Ten Kings .
The realm of Bharata is known as Bharātavarṣa in the Mahabhārata (the core portion of which is itself known as Bhārata ) and later texts. According to the text, the term Bharata is from the king Bharata, who was the son of Dushyanta and Shakuntala and the term varsa means a division of the earth or a continent.