Goddess Parvati was named also as Kali after birth by her father Himachala due to her complexion as mentioned in chapter 7 of Parvati Khanda in Shiva Purana.
गतस्तत्र गिरिः प्रीत्या सपुरोहितसद्विजः। ददर्श तनयां तां तु शोभमानां सुवाससा।।6।।
The mountain king accompanied with the priest as well as the Brahmanas went to see the girl who was self illumining.
नीलोत्पलदलश्यामा सुद्युर्ति सुमनोरमाम्। दृष्ट्रा च तादृशीं कन्यां मुमोदातिगिरीश्वरः।।॥7॥
She had the reflection of the blue lotus flowers, looking quite charming with beautiful complexion. The mountain king was immensely pleased by looking at her.
अथो शुभमुहूर्तेऽस्मिन् हिमवान्मुनिभिः सह। नामाकरोत्सुतायास्तु कालीत्यादि सुखप्रदम्॥11॥
Thereafter in the auspicious time, Himacala, in the company of the sages, gave the daughter the pleasant name of Kali.
Later Goddess Parvati did hard penance for Brahma to achieve fair complexion & named as Gauri. Plot was necessary for death of Shumbh Nishumbh by Kaushiki.