ayam hi rohini-putro
ramayan suhrdo gunaih
akhyasyate rama iti
baladhikyad balam viduh
sankarsanam usanty api
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
Garga Muni said: This child, the son of Rohini, will give all happiness to His relatives and friends by His transcendental qualities. Therefore He will be known as Rama. And because He will manifest extraordinary bodily strength, He will also be known as Bala. Moreover, because He unites two families Vasudeva’s family and the family of Nanda Maharaja — He will be known as Sankarsana.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
Baladeva was actually the son of Devaki, but He was transferred from Devaki’s womb to that of Rohini. This fact was not disclosed. According to a statement in the Hari-vamsa:
pratyuvaca tato ramah
sarvams tan abhitah sthitan
yadavesv api sarvesu
bhavanto mama vallabhah
Garga Muni did disclose to Nanda Maharaja that Balarama would be known as Sankarsana because of uniting two families — the yadu-vamsa and the vamsa of Nanda Maharaja — one of which was known as ksatriya and the other as vaisya. Both families had the same original forefather, the only difference being that Nanda Maharaja was born of a vaisya wife whereas Vasudeva was born of a ksatriya wife. Later, Nanda Maharaja married a vaisya wife, and Vasudeva married a ksatriya wife. So although the families of Nanda Maharaja and Vasudeva both came from the same father, they were divided as ksatriya and vaisya. Now Baladeva united them, and therefore He was known as Sankarsana.