Other than in Matsyapurana, all Puranas say the same thing about the naming of our land. Svayambhuba Manu had a son called Priyabrata. His son is Agnidhra and his son is Nabhi. Rishabh is the son of Nabhi. Rishabh had one hundred sons. the eldest of them was Bharat and he became king after his father. The land came to called Bharatvarsha after him. SrimadBhagabat says:
Priyabratam nama suto manoh Svayambhubasya yah.
Tasyagnidhrastato Nabhih Rishabhastatsutah smritah.
Abatirnam putrashatam tasyasid Brahmaparagam
Tesham boi Bharato jyestho Narayanaparayanah.
Bikhyatam varshametad yannanma Bharatamuttamam.
According to Kalidas, India was named Bhaarata due to Bharata the son of Dushyanta. This view is however not supported by the Puranas.