Lord Balarama
Shri Garga Muni explains the name of Lord Balarama: The yogis find their happiness (ramante) in Him, or he is the greatest enjoyer (ramati), or with His transcendental qualities He delights (ramayati) the devotees. For these reasons the sages know Him as Rama. Because He was pulled (sankarshana) from the womb He is also known as Sankarshana. Because when the universe is annihilated He alone remains (avashesha), the sages know Him as Shesha. Because He is extremely strong (bala), they know Him as Balarama.
The Story of Shesha
During the Cakshusha-manvantara Prajapati Daksha gave his eleven beautiful daughters in marriage to Kashyapa Muni.
Kadru was the best of them. In Krishna Lila Kadru appeared as Rohini. She is dear to Maharaja Vasudeva. Lord Balarama was born as her son.
Kadru gave birth to many millions of great, powerful, invincible jewel-decorated, and very poisonous snakes, some having five-hundred heads, and others having a hundred heads.
Ananta Shesha, the king of snakes, who is greater than the greatest, was the first of them. In Krishna Lila Ananta is Balarama, the elder brother of the infallible Supreme Personality of Godhead.
One day Lord Krishna, the Supreme Personality of Godhead, who is beyond the world of matter and is always happy at heart, with words like the rumbling of clouds, spoke to Ananta Shesha.
The Supreme Personality of Godhead said: “No one else has the power to hold up the planets of Bhu-mandala. You please carry these planets on Your head.”
“Your power is endless, and therefore You are known as Ananta (the endless). Please accept this duty for the welfare of the people.”
Shri Shesha said: O Lord, please put some limit on how long I must hold the world. Then, according to Your word, I will hold up Bhu-mandala.”
The Supreme Personality of Godhead said: “O king of snakes, with Your thousand mouths always chant My names, names that reveal My transcendental qualities. When You come to the end of all My transcendental names You can put down the burden of Bhu-mandala and relax.”
Shri Shesha said: “I will hold up Bhu-mandala. But who will hold Me up? Without support how can I stand in the water? O Lord, please tell Me.”
The Supreme Personality of Godhead said: “I will become a turtle and then I will hold You up. O My friend, don’t be unhappy to hold such a great burden for such a long time.”
Then Lord Shesha rose, bowed down before Lord Krishna who holds the flag of Garuda, and went eight hundred thousand miles below Patalaloka
Then very powerful Ananta Shesha picked up Bhu-mandala and held it in one hand.
When Sankarshana Ananta went to Patalaloka, by Brahma’s order the other great snakes followed Him. Some went to Atalaloka and others to Sutalaloka, Mahatalaloka, Talatalaloka, and Rasatalaloka.
Many snakes headed by Kaliya happily lived in Ramanaka-dvipa, the home Brahma gave to them.
Lord Śrī Nityānanda
It is explained in Sri Caitanya-Caritamrta Adi-Lila Chapter 5:
That original Lord Kṛṣṇa appeared in Navadvīpa as Lord Caitanya, and Balarāma appeared with Him as Lord Nityānanda.
May Śrī Nityānanda Rāma be the object of my constant remembrance. Saṅkarṣaṇa, Śeṣa Nāga and the Viṣṇus who lie on the Kāraṇa Ocean, Garbha Ocean and ocean of milk are His plenary portions and the portions of His plenary portions.
Lord Balarāma is the original Saṅkarṣaṇa. He assumes five other forms to serve Lord Kṛṣṇa.
He Himself helps in the pastimes of Lord Kṛṣṇa, and He does the work of creation in four other forms.
He executes the orders of Lord Kṛṣṇa in the work of creation, and in the form of Lord Śeṣa He serves Kṛṣṇa in various ways.
Srila Prabhupada explains in Purport :
According to expert opinion, Balarāma, as the chief of the original quadruple forms, is also the original Saṅkarṣaṇa. Balarāma, the first expansion of Kṛṣṇa, expands Himself in five forms: (1) Mahā-saṅkarṣaṇa, (2) Kāraṇābdhiśāyī, (3) Garbhodakaśāyī, (4) Kṣīrodakaśāyī, and (5) Śeṣa. These five plenary portions are responsible for both the spiritual and material cosmic manifestations. In these five forms Lord Balarāma assists Lord Kṛṣṇa in His activities. The first four of these forms are responsible for the cosmic manifestations, whereas Śeṣa is responsible for personal service to the Lord. Śeṣa is called Ananta, or unlimited, because He assists the Personality of Godhead in His unlimited expansions by performing an unlimited variety of services. Śrī Balarāma is the servitor Godhead who serves Lord Kṛṣṇa in all affairs of existence and knowledge. Lord Nityānanda Prabhu, who is the same servitor Godhead, Balarāma, performs the same service to Lord Gaurāṅga by constant association.
In all the forms He tastes the transcendental bliss of serving Kṛṣṇa. That same Balarāma is Lord Nityānanda, the companion of Lord Gaurasundara.
I surrender unto the lotus feet of Śrī Nityānanda Rāma, who is known as Saṅkarṣaṇa in the midst of the catur-vyūha [consisting of Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha]. He possesses full opulences and resides in Vaikuṇṭhaloka, far beyond the material creation.