Haribaṁśa (Haribamsa) explains the word Ekānaṁśā (Ekanamsa) in the following way-

Though Ekānaṁśā (Ekanamsa) was born from a part of Lord Viṣñu (Vishnu), the saviour of his subjects, conceptually and by nature, she was one and all. She was the Māyāśakti (Mayasakti or feminine power) of the Lord- Yogamāyā (Yogamaya)-

Viddhi caināmathotpannāthaṁśāddevīṃ prajāpateḥ.

Ekānaṁśāṃ yogakanyāṃ rakṣārthaṃ keśavasya tu.

The explanation of the name, Ekānaṁśā (Ekanamsa) was given in more details in the Devīpurāṇa. Here it is said- she encompasses all the spaces. She is alone in one sense. In another sense, she is not alone, rather she has many manifestations. She is not a part of anyone. She is complete-

Ete asate ca lokā na ekā na ca sā smṛtā.

Ekā cā nāṃśato lokā ekānaṁśā ca sā smṛtā.

According to the Haribaṁśa (Haribamsa), the girl who was just born to Nanda and Yaśodā (Yasoda) during the same time when Kṛṣña (Krishna) was born, was carried by Vasudeva to Devakī (Devaki) in the prison of Kaṁsa (Kamsa). This girl was Ekānaṁśā (Ekanamsa). When Kaṁsa (Kamsa) threw her on the stone, she emerges in the sky as a beautiful goddess- her hair was open, she exuded divine scent-

Nīlapītāṁvaradharā gajakuṁbhopastanī.

Rathavistīrṇajaghanā candravaktrā caturbhujā.

Vidyudvispaṣṭavarṇābhā vālārkasadṛśekṣaṇa.

This manifestation of Ekānaṁśā (Ekanamsa) is actually another epitome of Devī Durgā (Devi Durga). In the Bhāgavata Purāṇa (Bhagavata Purana), Viśvātmā Bhagavāna (Visvatma Bhagavana) ordered Yogamāyā (Yogamaya) to be incarnated into the womb of Yaśodā (Yasoda) in the  Brajamaṇḍala (Brajamandala) for facilitating Kṛṣṇāvatāra (Krishnavatara), even before  Kṛṣaṇa took the avatāra (avatara or god taking human incarnation) in this earth-

Tvaṃ yaśodāyāṃ nandapatnyāṃ bhaviṣyasi.

This order was accompanied with the list of incarnations in which this Ekānaṁśā Yogamāyā (Ekanamsa Yogamaya) would be worshiped in this earth-

Durgeti bhadrakālīti vijayā vaiṣñavīti ca.

Kumudā caṇḍikā kṛṣñā mādhavī kanyaketi.

Māyā nārāyaṇīśānī śāradetyamviketi ca.

It means that Ekānaṁśā  (Ekanamsa) can be synonymous with these names  of Durgā (Durga).

In the Haribaṁśa (Haribamsa), Kaṁsa (Kamsa), who was afraid of Kṛṣña (Krishna), got the news from Nārada (Narada) that the baby girl whom Kaṁsa (Kamsa) killed by throwing her onto the stones, helped in replacing herself with Kṛṣña (Krishna) and taking away Kṛṣña (Krishna) to another place immediately after his birth by divine māyā or magical power-

Rātrou vyāvartitāvetou garbhou.

This divine woman who was born out of the womb of Yaśodā (Yasoda) then lived in the Vindhya Parvata. She killed the two demons called Śuṁbha and Niśuṁbha (Sumbha and Nisumbha) and established herself there. Bhūtasaṁgha (Bhutasamgha) encircled her and took care of her. All the dacoits and demons worshiped her incarnation there. She was embellished with the pots of alcohol and two pots full of meat. She was bejeweled with the dress and jewelries made of the peacock tails.

In the Mahābhārata (Mahabharata), Yudhiṣṭhira (Yudhishthira) performed the Durgā stava (Durga stava or the song eulogizing Durga). This song reinforced that this Vindhyavāsinī Devī (Vindhyavasini Devi or the goddess who lived in the Vindhya Parvata) described in the Harivaṁśa (Harivamsa) was actually Nārāyanī Devī Durgā (Narayani Devi Durga) and she became one with Ekānaṁśā Bhagavatī (Ekanamsa Bhagavati). In this Durgā stava (Durga stava), the name of Ekānaṁśā (Ekanamsa) was not mentioned but the different characteristics of the goddess is of Ekānaṁśā (Ekanamsa). Here also, she was born in the womb of Yaśodā (Yasoda), and she belonged to the Nandagopakula. She terrified Kaṁsa (Kamsa) and the other Asuras were slain by her. She was the sister of Vāsudeva Kṛṣña (Vasudeva Krishna)- adorned with divine necklace and holding Khaḍga (Kharga) and Kheṭaka (Khetaka).

This Bhagavatī Devī (Bhagavati Devi), the sister of Vāsudeva Kṛṣña (Vasudeva Krishna), was the human manifestation of Śakti (Sakti) and the concept of Śaktimat (Saktimat) in philosophical treatise. On the other hand, Ekānaṁśā (Ekanamsa) as an eternal Vaiṣñavī (Vaishnavi) power occupied the middle position between Jagannātha (Jagannatha) and Valarāma (Valarama) as their sister, Subhadrā (Subhadra). Varāhamihira In Vṛhat Saṁhitā (Vrihat Samhita), (Varahamihira) indicates the place of Ekānaṁśā (Ekanamsa) in between Jagannātha (Jagannatha) and Valarāma (Valarama)-

Ekānaṁśā kāryā devī valadevo- kṛṣñayo madhye.

So it indicates the place of Subhadrā (Subhadra) and therefore, Subhadrā (Subhadra) is synonymous with Ekānaṁśā (Ekanamsa).

[Vrihat Samhita 58.37; See The Sakti Cult and Tara, Ed. D. C. Sircar, p. 84].

In the Skanda Purāṇa (Purana), Ekānaṁśā (Ekanamsa) was a part of Kālī- Pārvatī (Kali-Parvati). She was synonymous here with Kālī (Kali). In this Purāṇa (Purana), it was said- Brahmā (Brahma) asked Niśā Devī (Nisa Devi) to blacken the complexion of Pārvatī (Parvati) who was then in the womb of Menā. Then he uttered a prophesy- When Pārvatī (Parvati) will be Gourī (Gouri) by the power of meditation, Niśā Devī (Nisa Devi) will attain the same status of Pārvatī (Parvati). Then Niśā (Nisa) will be called Ekānaṁśā Gourī (Ekanamsa Gouri).Being adorned by the rūpāṁśa (rupamsa or the beauty parts), Niśā (Nisa) will be Umā (Uma). And the earlier Niśā (Nisa) will be worshiped as Ekānaṁśā (Ekanamsa)-

Rūpāṁśena ca saṁyuktā tvamumākhyā bhaviṣyasi .
Ekānaṁśeti lokastvāṃ varade pūjayiṣyati.

It is to be noted that in the Haribaṁśa (Haribamsa), Vindhyavāsinī Devī (Vindhyavasini Devi) was represented to be fond of alcohol and meat. Here in the Skanda Purāṇa (Purana), Ekānaṁśa (Ekanamsa) who was synonymous with Kālī (Kali) was also seen to accept the gifts of alcohol and meat and to fulfill the desire of her devotees. On the day of Mahānavamī (Mahanavami or the auspicious ninth day), mahiṣ or meṣ (mahish or buffalo) was sacrificed while worshiping Ekānaṁśa (Ekanamsa). Again in the Padma Purāṇa (Purana), it was clearly narrated in the Sṛṣṭikhaṇḍa (Srishtikhanda) that Ekānaṁśa (Ekanamsa) was created from the black skin of Pārvatī Kālī (Parvati Kali) and was ordered by Brahmā (Brahma) to live in the Vindhya Parvata. There she became famous as Vindhyavāsinī (Vindhyavasini). On the other side it can be noted that Kālī (Kali) left her black cells from her skin and became Kouśikī Kālī (Kousiki Kali). Ekānaṁśa (Ekanamsa) was also synonymous with this Kouśikī Kālī (Kousiki Kali).

Sukumar Sen comments that the actual spelling of the word ‘Ekānaṁśā’ (Ekanamsa) should be ‘Ekānaṁsa’ (Ekanamsa). According to him, ‘Ekānaṁsa’ (Ekanamsa) means unmarried Kumārī Devī (Kumari Devi)- “The name as it means Single (eka) and unshared (an-amsa, i.e. unmarried). The correct reading of the name seems to be Ekānamśa (Lone and virgin goddess)”. But later, these two names, Ekānaṁśā (Ekanamsa) and Ekānaṁsā’ (Ekanamsa) became extinct and the goddess came to be known by the names of Bhadrā (Bhadra) and Subhadrā (Subhadra). Dr. Sen thinks that Umā Haimavatī (Uma Haimavati) and Ekānaṁśā (Ekanamsa) of the Kenopaniṣada (Kenopanishada) were associated with Vedic Uṣā (Usha) and Aditi.

[Sukumar Sen, The Great Goddess in Indian Tradition, pp.30, 57].

In the Vṛhat Saṁhitā (Vrihat Samhita) of Varāhamihira (Varahamihira), the epitome of Goddess Ekānaṁśā (Ekanamsa) sometimes had two hands, sometimes she had four hands. She was also represented as having eight hands. When the Goddess had two hands, her one hand was on the hips and the other hand held a lotus flower. The Goddess could also be represented as having four hands. Then her left hands carried a book and a lotus flower. One of right hands present the Varadamudrā (Varadamudra) which wiped out all the fears. Her lower right hand carried the Akṣasūtra (Akshasutra). when the Goddess had eight hands, her left hands carried kamaṇḍalu (Kamandalu or a kind of pitcher), bow, lotus flower and scriptural books. And her right hands carried Varadamudrā (Varadamudra), arrows, darpaṇa (darpana or a kind of mirror) and Akṣasūtra (Akshasutra).

[Vrihat Samhita 58.37-39.