One day, Nanda Maharaja requested Gargamuni, the family priest to visit their home in order to give names to Krishna and Balarama. When Gargamuni arrived at his house Nanda Maharaja, received him very well and then requested him to perform the naming ceremony. Gargamuni then reminded Nanda Maharaja that Kamsa was looking for the son of Devaki and said that if he performed the ceremony very opulently it would come to the notice of Kamsa, who would then suspect that Krishna was the son of Devaki. Nanda Maharaja therefore asked Gargamuni to perform the ceremony in secret, and Gargamuni did so giving the reasons for Balarama's names as follows:

""Because Balarama, the son of Rohini, increases the transcendental bliss of others, His name is Rama, and because of His extraordinary strength, He is called Baladeva. He attracts the Yadus to follow His instructions, and therefore His name is Sankarshana."" Bhagavata Purana 10.8.12

Balarama in Gaudiya Vaishnava belief
In Bhagavata Purana
Birth
Balarama worship