If Rishabanatha was the first Tirthankar then why was his son Bharata so famous that India is called Bharata after his name. What was the reason of his glory?
India was named after Rishabha's son Bharata because he conquered it, as described in _this chapter of the Srimad Bhagavatam:
My dear King, Bharata Mahārāja was a topmost devotee. Following the orders of his father, who had already decided to install him on the throne, he began to rule the earth accordingly. When Bharata Mahārāja ruled the entire globe, he followed the orders of his father and married Pañcajanī, the daughter of Viśvarūpa. Just as the false ego creates the subtle sense objects, Mahārāja Bharata created five sons in the womb of Pañcajanī, his wife. These sons were named Sumati, Rāṣṭrabhṛta, Sudarśana, Āvaraṇa and Dhūmraketu. Formerly this planet was known as Ajanābha-varṣa, but since Mahārāja Bharata’s reign it has become known as Bhārata-varṣa. Mahārāja Bharata was a very learned and experienced king on this earth. He perfectly ruled the citizens, being himself engaged in his own respective duties. Mahārāja Bharata was as affectionate to the citizens as his father and grandfather had been. Keeping them engaged in their occupational duties, he ruled the earth.
Note that Prabhupada's translation renders the word "varsha" as planet. That's because ISKCON considers Bharatavarsha to be the entire Earth, Jambudvipa as something even bigger than that, etc. But most other Hindus, myself included, believe that the seven Dvipas are the seven continents, Jambudvipa is the continent India is located in, Bharatavarsha refers to the Indian subcontinent, etc.