Ahirvudhnya is one of the Aṣṭottara Sahasranāma (Ashtottara Sahasranama; Thousand and eight names)) of Śiva-Mahādeva (Siva-Mahadeva). In Purāṇa (Purana; Mythological Scripture), Ahirvudhnya denotes gṛhapti (grihapati) agni or gārhapatya agnisthāna (garhapatya agnisthana, a ritual fireplace considered sacred for the life of a householder). Again, Ahirvudhnya is one of the eleven Rudra(s) born of the womb of Surabhī (Surabhi), sired by Kaśyapa Prajāpati (Kasyapa Prajapati; Kasyapa as a Ruler of the people), and by the boon of Mahādeva (Mahadeva).
The concept behind the naming of Gārhapatya agni as Ahirvudhnya, lies in Vājasaneyī Saṃhitā (Vajasaneyi Samhita). Here, in the main mantra it is said, ahirasi vudhnya. In explaining the mantra, an ancient commentator like Mahīdhara (Mahidhara) has said that — the gārhapatya agni that is established at the west of patnīśālā, is called Ahirvudhnya. The term ahi means something that has no decline. The newly established gārhapatya agni does never extinguish, nor is it allowed to be extinguished. According to the mythological conception, God Śiva’s name Ahirvudhnya can be interpreteted in terms of his manifestation as agni (fire ), or in terms of his affinity with one of the eleven Rudra(s).
Besides, explaining the meaning of Ahirvudhnya, Nīlakaṇṭha (Nilakantha), the commentator of Mahābhārata (Mahabharata), has written —
ahiḥ sarpaḥ tasya viśeṣaṇaṃ vudhnyaḥ vudhnyeḥ
mūle sādhuriti brahmāṇḍamūlaṃ pātālaṃ
tatra vartataiti yāvat, śeṣa svarūpa ityarthaḥ.
According to Nīlakaṇṭha’s conception, ahi means ‘snake’, and vudhnya means the root or base. One who resides at the base of the universe, that is, Pātāla (Patala; the netherworld), and holds the entire universe on his thousands of hoods — is Ahirvudhnya, and this indicate Anantanāga (Anantanaga; the mythical great serpent who holds the universe). God Śiva, like Anantanāga, holds the entire universe, too. So he is called Ahirvudhnya.