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In the answer to my question, I learned about the name 'Kalaka'. But, who is Kalaka?
I found some background behind Shiva, Parvati, and Bhairava's incarnations, Mahesha, Sarada and Vaitala in this chapter of Shiva Purana. Is there any other information about them in any scriptures?
Kalaka is a powerful Gaṇa. (A gaṇa is a deity associated with Lords Shiva and Ganesha; they live at Kailasa.)
Shiva Purana 2.2.33 says:
O sage, Kuṇḍī the most excellent of the Gaṇas and Parvataka went each with twelve crores in order to destroy Dakṣa’s sacrifice:
Kāla, Kālaka and Mahākāla went to the sacrifice of Dakṣa with a hundred crores.
and 2.1.20 says:
15-16. Viṣṭambha and Candratāpana each with eight crores, the leader of Gaṇas Mahākeśa with a thousand crores.
Kuṇḍin, Vāha and the auspicious Parvataka with twelve crores each, Kāla, Kālaka and Mahākāla each with a hundred crores.
Agnika with a hundred crores, Abhimukha with a crore, Ādityamūrdhā and Dhanāvaha each with a crore.
Sannāha and Kumuda with a hundred crores, Amogha, Kokila and Sumantraka each with a crore.
Your Shiva Purana story seems to be the only place where Mahesha, Sarada, and Vaitala are mentioned, though a line in the same Purana treats 'Mahesa' as another name for Shiva. Otherwise, these avatars are never again mentioned.
Obeisance to Thee, O lord, from whom the mobile and the immobile beings have originated. Obeisance to the great Puruṣa, Maheśa, the supreme Īśa and the great Ātman. [2.2.15]
