Ananta is another name of Sesha. Vishnu Purana confirms it here.
Below the seven Pátálas is the form of Vishńu, proceeding from the quality of darkness, which is called Śesha, the excellencies of which neither Daityas nor Dánavas can fully enumerate. This being is called Ananta by the spirits of heaven, and is worshipped by sages and by gods.
The names of most snakes are mentioned in the Astika Parva of Mahabharata. All the nagas are brothers of Sesha
Sauti said, O thou whose wealth is asceticism, from fear of being lengthy, I shall not mention the names of all the snakes. But I will recite the names of the chief ones. Listen to me!
"Sesha was born first, and then Vasuki. (Then were born) Airavata, Takshaka, Karkotaka, Dhananjaya, Kalakeya, [...] Samkha, Valisikha, Nisthanaka [...] Padma, Mahapadma, Sankhamukha, Kushmandaka, Kshemaka, [...] Kauravya, Dhritarashtra, Sankhapinda, Virajas, Suvahu, Salipinda, Prabhakara, Hastipinda [...]
Still, for the sake of being specific, I shall attempt to give info about all the nine snakes.
Padmanabha is a righteous snake king; his story is in Santi Parva of Mahabharata
In that forest which is known by the name of Naimisha, and which is situated on the banks of the Gomati, there is a city called after the Nagas.
A mighty Naga, of righteous soul, dwells in the city that stands in that region. That great Naga is known by the name of Padmanabha or Padma. Walking in the triple path (of acts, knowledge, and adoration) he gratifies all creatures in thought, word, and deed.
He's also said to have pulled the chariot of Sun God.
The wife of the Naga said, 'Reverend sir, my husband has gone to drag the car of Surya for a month. O learned Brahmana, he will be back in fifteen days, and will, without doubt show himself unto thee.
Kambala is referenced in Harivamsa.
He (akrUra) saw, the king of serpents (sheSha), the lord of ekArNava (ocean at the time of deluge), being worshipped by great serpents (having split tongues) such as vAsuki.
Serpents named Kambala and Ashvataru were fanning the king of serpents, the lord, seated on the righteous seat.
He's also said to have attended Varuna's Sabha in Mahabharata along with other Nagas.
And Vasuki and Takshaka, and the Naga called Airavana; Krishna and Lohita; Padma and Chitra endued with great energy; the Nagas called Kamvala and Aswatara; and Dhritarashtra [...]--all having auspicious marks and mandalas and extended hoods;--these and many other snakes. O Yudhishthira, without anxiety of any kind, wait upon and worship the illustrious Varuna.
Takshaka is referenced numerous times in the Mahabharata. He stole amrita earrings from Uttanka the disciple of Dhaumya
"On the road Utanka perceived coming towards him a naked idle beggar sometimes coming in view and sometimes disappearing. And Utanka put the ear-rings on the ground and went for water. In the meantime the beggar came quickly to the spot and taking up the ear-rings ran away. And Utanka [...] pursued the thief with the utmost speed. And having with great difficulty overtaken him, he seized him by force.
But at that instant the person seized, quitting the form of a beggar and assuming his real form, viz., that of Takshaka, speedily entered a large hole open in the ground. And having got in, Takshaka proceeded to his own abode, the region of the serpents.
And was responsible for the death of King Parikshit.
And as the king was smiling, Takshaka, who had (in the form of that insect) come out of the fruit that had been offered to the king, coiled himself round the neck of the monarch. And quickly coiling round the king's neck and uttering a tremendous roar, Takshaka, that lord of snakes, bit that protector of the earth.'"
And the mansion in which the king was living blazed up with Takshaka's poison. And the king's councillors, on beholding it, fled away in all directions. And the king himself fell down, as if struck by lightning.