The Goddess whom we call Parvati or Durga is actually known as Goddess Adi Shakti or simply as Shakti.
Maa Durga has nine major forms, known as Nav Durga.
• Maa Shailputri
◦ After her self-immolation, Goddess Parvati took birth as Lord Himalaya's daughter. In this form, she was Maa Shailputri. In Sanskrit, Shail means mountain. Hence, Shailputri means the daughter of the mountain. Goddess Shailputri is worshipped on the first day of Navratri.
• Maa Brahmacharini
◦ Maa Parvati took birth at the home of Daksha Prajapati after her Kushamnada form. Goddess Parvati was a great Sati in this avatar, and her unmarried form was worshipped as Goddess Brahmacharini. The Goddess governs Lord Mangal, the provider of all fortunes. She did great penance to attain Lord Shiva as her husband. During her penance, she spent 1,000 years on a diet of flowers and fruits and another 100 years on leafy vegetables while sleeping on the floor.
• Maa Chandraghanta
◦ Goddess Chandraghanta is the married avatar of Maa Parvati. After marrying Lord Shiva, the Goddess adorned her forehead with a half or crescent moon and was known as Maa Chandraghanta. She governs Shukra and is worshipped on the third day of Navratri.
• Maa Kushmanda
◦ Goddess Parvati started living inside the Sun's centre after taking the Siddidatri form so the Sun could release energy to the universe. Maa Kushmanda has the power and capability to live inside the Sun, and the glow and radiance of her body are as luminous as that of the Sun. The Goddess has eight hands and is known as Ashtabhuja Devi.
• Maa Skandamata
◦ When Goddess Parvati became Lord Skanda/Lord Kartikeya's mother, she was known as Maa Skandamata. Devotees who worship this form of Goddess Parvati also get the blessings of Lord Kartikeya. Goddess Skandamata mounts the ferocious lion and carries baby Murugan in her lap. She also sits on the Lotus flower and is known as Goddess Padmasana.
• Maa Katyayani
◦ To destroy the demon Mahishasura, Goddess Parvati took the form of Goddess Katyayani. It was the most violent form of Goddess Parvati, also known as Warrior Goddess. Maa Katyayani is worshipped on the sixth day of Navratri. According to Drik Panchang, Goddess Parvati was born at the home of sage Katya and due to this, this form of Goddess Parvati is known as Katyayani.
• Maa Kalaratri
◦ When Goddess Parvati removed her golden skin to kill the demons Shumbha and Nishumbha, she was known as Goddess Kalaratri. She is known as the fiercest form of Goddess Parvati. Maa Kalaratri's complexion is dark, and she rides on a donkey. She is depicted with four hands - her right hands are in Abhaya and Varada Mudra, and her left hands carry a sword and the deadly iron hook.
• Maa Mahagauri
◦ At the age of sixteen, Goddess Shailputri was extremely beautiful and blessed with a fair complexion. Due to this, she was known as Goddess Mahagauri. She governs the planet, Rahu. Due to her fair skin tone, Goddess Mahagauri is compared with the conch, the moon and the white flower of Kunda. She is also known as Shwetambardhara, as she only wears white clothes.
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• Maa Siddhidatri
◦ According to Hindu scriptures, Lord Rudra prayed to the formless Adi-Parashakti - the supreme Goddess of Power - at the universe's beginning for creation. She appeared in the form of Maa Siddhidatri from the left half of Lord Shiva, after which Lord Shiva got the name Ardha-Narishwar. She is the Goddess who possesses and bestows all types of Siddhis to her devotees.
The first form of Goddess Durga (Shailputri), means Daughter of mountains (Shail means Parvat, so she is Parvat ki Putri). So, since she is Parvat ki putri.. she is called Parvati. That’s why Goddess Durga is Parvati. I hope my answer will help you, thank you and have a nice day ahead.