He (the son of Rohini) will be called Rama because of His ability to please all the inhabitants of Gokula, and He will be known as Balabhadra because of His extensive physical strength - SB 10.2.13

Expressions researched:
"He will be called Rāma because of His ability to please all the inhabitants of Gokula, and He will be known as Balabhadra because of His extensive physical strength"

Srimad-Bhagavatam

SB Canto 10.1 to 10.13

The son of Rohiṇī will also be celebrated as Saṅkarṣaṇa because of being sent from the womb of Devakī to the womb of Rohiṇī. He will be called Rāma because of His ability to please all the inhabitants of Gokula, and He will be known as Balabhadra because of His extensive physical strength.

SB 10.2.13, Translation and Purport

The son of Rohiṇī will also be celebrated as Saṅkarṣaṇa because of being sent from the womb of Devakī to the womb of Rohiṇī. He will be called Rāma because of His ability to please all the inhabitants of Gokula, and He will be known as Balabhadra because of His extensive physical strength.

These are some of the reasons why Balarāma is known as Saṅkarṣaṇa, Balarāma or sometimes Rāma. In the mahā-mantra—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—people sometimes object when Rāma is accepted as Balarāma. But although devotees of Lord Rāma may object, they should know that there is no difference between Balarāma and Lord Rāma. Here Śrīmad-Bhāgavatam clearly states that Balarāma is also known as Rāma (rāmeti). Therefore, it is not artificial for us to speak of Lord Balarāma as Lord Rāma. Jayadeva Gosvāmī also speaks of three Rāmas: Paraśurāma, Raghupati Rāma and Balarāma. All of them are Rāmas.