Āvartamānebhyovapuḥ (Avartamanebhyavapuh) is one of the Thousand and Eight Names of Śiva. In Śivasahasranāmastotra (Sivasahasranamastotra) of Mahābhārata (Mahabharata), while the other editions maintain the reading ‘vapurāvartamānebhyaḥ‘ , the edition by Haridāsa Siddhāntavāgiśa (Haridasa Siddhantabagisa) maintains the reading ‘vasudhā vartamānejyo‘. So, Siddhāntavāgiśa has considered the two names, Vasudhā and Vartamānejya, instead of ‘Āvrtamānebhyo vapuḥ’. Here we are are going to discuss both readings.
In course of commenting on the name ‘Āvartamānebhyo vapuḥ’ Nīlakaṇṭha (Nilakantha), the commentator of Mahābhārata, has said,
vapuḥ vapuḥ pradātā avartamānebhyaḥ svargacyutebhyaḥ.

Here ‘svargacyuta’ (svargachyuta; fallen from heaven) refers to those who have not yet attained salvation, or have not been freed from the cycle of birth and death. These souls, after death, leaves their corporeal frames and go to paraloka (the other world) and there, having experienced the results of the virtues and vices committed by themselves, take a rebirth. Those jīvātmā (jivatma; souls of mortal beings) who take rounds in the cycle of ‘punarapi jananaṁ punarapi maraṇaṁ punarapi jananī jaṭhare śayanaṁ‘ (to be born again, to die again, and again to lie in the mother’s womb) are called āvartamāna (on the round).

During the cycle of rebirth, the Supreme Being, Mahādeva, provides the āvartamāna jīvātmā with new vapu or śarira (sarira; corporeal body ) , hence He is addressed as ‘Āvartamānebhyo vapuḥ’.

Nīlakaṇṭha has mentioned another reading of the śloka (sloka; verse) — ‘vasurāvartamānebhyaḥ’ — though we have not found this in any edition. In this reading, the meaning would be thus : One who bestows ‘vasu’ or wealth upon those who are bound to the cycle of saṁsāra (samsara; worldly life) —
vasuriti pāthe sevakebhyo dhanaprada ityarthaḥ.
We have already mentioned that Haridāsa Siddhantavāgiśa has taken into account both names– ‘Vasudhā’ (Vasudha) and ‘Vartamānejya’ (Vartamanejya).

While describing the meaning of the name Vasudhā (Vasudha), he says,
vasu tejo dadhātīti vasudhā.
One meaning of the name vasu may be teja or dīpti (energy, imaged as flame, illumination). Mahādeva holds all teja (energy) or vasu manifested in the world, so his name is Vasudhā (Vasudha). Analysing the term ‘Vartamānejya’, Siddhāntavāgiśa says,
vartamānā ijyā pujā jasya saḥ.

‘Ijya’ comes from ‘yaj’ dhātu (dhatu; root-verb) in Sanskrit. One who is worshiped is called ‘Ijya’. Mahādeva had been worshiped since the beginning of creation, and He is being worshiped till the present — hence the name, ‘Vartamānejya’.