Krishna was also called Bharata because of His all pervading nature. The meaning of this is that the aspect of Bharata is connected with Aditya and Aditya is in turn connected with Agni and therefore, if you want to control Agni, you have to put it only in another place where there is Agni. (SSB 1974, p. 185)

The name Arjuna means the one with a pure heart. Arjuna was always living in Krishna. A number of times Krishna referred to Arjuna as Bharata. This name means, ‘the one who lives in the effulgence of the divinity is Bharata. All the deeper aspects of the relationship of Krishna and Arjuna can be gleaned from the names that Krishna gave to Arjuna. (DBG, p. 157)