garbha-sankarsanat tam vai
prahuh sankarsanam bhuvi
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The son of Rohini will also be celebrated as Sankarsana because of being sent from the womb of Devaki to the womb of Rohini. He 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.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
These are some of the reasons why Balarama is known as Sankarsana, Balarama or sometimes Rama. In the maha-mantra Hare Krsna, Hare Krsna, Krsna Krsna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare people sometimes object when Rama is accepted as Balarama. But although devotees of Lord Rama may object, they should know that there is no difference between Balarama and Lord Rama. Here Srimad-Bhagavatam clearly states that Balarama is also known as Rama (rameti). Therefore, it is not artificial for us to speak of Lord Balarama as Lord Rama. Jayadeva Gosvami also speaks of three Ramas: Parasurama, Raghupati Rama and Balarama. All of them are Ramas.