Meaning and elaboration
Meaning: Distinguished as the Linga, the symbol of creation and dissolution.
Elaboration
Lingg'akhya Chaiva means "Distinguished as the Linga" or "Known by the Linga." This name presents Goddess Kali as embodying the divine principle of creation and dissolution, analogous to the Shiva Linga.
The Linga as a Cosmic Symbol The Linga is most closely associated with Shiva and signifies the formless supreme reality as well as the potent principle of creation and destruction. When Kali is described as Lingg'akhya, it means that she too is that ultimate reality: the source from which all manifestation arises and into which all dissolution returns. She is not secondary or derivative, but the very essence of both the unmanifest and manifest cosmos.
Union of Purusha and Prakriti In philosophical language, the Linga represents Purusha, consciousness or Shiva, while its base, the Yoni, represents Prakriti, the primordial creative energy. By being identified with the Linga, Kali is shown as the dynamic Shakti that awakens and activates consciousness. She is therefore the active principle behind the entire cosmic play, holding within herself both the Yoni and the awakened essence of the Linga.
The Immanent and Transcendent This name emphasizes Kali's absolute nature, which transcends all duality. Like the Linga, she is both formless, nirguna, and the source of all forms, saguna. She is the point of origin and the point of cessation, the seed of creation and the fire of dissolution. The entire spectrum of existence is gathered within her.
Beyond Gendered Interpretations To identify Kali with the Linga is also to move beyond limited gendered interpretation. It affirms her as the fundamental cosmic energy that exists prior to all differentiation and gives rise to it. In this way she is revealed as Supreme Brahman, embracing within her boundless being every principle: masculine and feminine, stillness and dynamism, transcendence and manifestation.