Garga Muni said: This child, the son of Rohiṇī, will give all happiness to His relatives and friends by His transcendental qualities. Therefore He will be known as Rāma. 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 Mahārāja — He will be known as Saṅkarṣaṇa.
Srimad Bhagavata Purana
श्रीमद्भागवतमहापुराणम्
मूल श्लोकः
गर्ग उवाच । अयं हि रोहिणीपुत्रो रमयन् सुहृदो गुणैः । आख्यास्यते राम इति बलाधिक्याद्बलं विदुः । यदूनामपृथग्भावात्सङ्कर्षणमुशन्त्युत
garga uvāca | ayaṃ hi rohiṇīputro ramayan suhṛdo guṇaiḥ | ākhyāsyate rāma iti balādhikyādbalaṃ viduḥ | yadūnāmapṛthagbhāvātsaṅkarṣaṇamuśantyuta
SB 10.8.12