The term ‘Īśa’ (Isa) generally denotes one who authorises, controls or rules, one who is entitled to own, and so on. In this sense, terms like Nareśa (Naresha; lord of men), Sureśa (Suresa, lord of the gods), Kṣitīśa (kshitisa; ruler of the earth), Gaṇeśa (Ganesa; ruler of the people), Śrīśa (Srisa, lord of Sri or Goddess Lakshmi), Dvārakādhīśa(Dwarakadhisa; Lord of Dwaraka) — are rather understandable. Again, in Mahābhārata (Mahabharata), when Saṁvaraṇa (Samvarana) sought to convince Tapatī (Tapati) to marry him following the Gāndharva (Gandharva) rites, she said, — I am not the master of this maiden-body of mine —
na cāhaṁ īśa dehasya.
Here, too, ‘Īśa’ does not refer to anything specific. But in a specific sense, Īśa refers to Mahādeva (Mahadeva) or Śiva (Siva). This can be found in the nāndīśloka of Abhijñānaśakuntalam (Abhijnanasakuntalam) by Kālidāsa (Kalidasa), as well as in such a lexicon-like text Trikāṇḍaśeṣa by Puruṣottamadeva (Purushottamadeva). Here it is said that, Īsa’ refers to the ‘lord’ or master as well as Mahādeva — prabhuśaṅkarayorīśaḥ.
Similarly, it is said in Medinīkoṣa(Medinikosha) —
īśaḥ prabhau mahādeve.
In Virātaparva of Mahābhārata, Īśa-Mahādeva was one of those gods who assembled in different vimānas(vimana, celestial vehicles) in order to behold the battle between Arjuna and the Kaurava. The Īśa whose pratimālakṣaṇa (pratimalakshana; image-characteristics) have been described in Matsyapurāṇa (Matsyapurana), is obviously śūlapāṇi (sulapani; one who holds the sula-weapon) Mahādeva, and the understanding that Īśa specifically denotes Mahādeva is also evident from this declaration of Purāṇa (Purana)–now we are discussing the image-characteristics of Īśa — and immediately after this, it describes the features of the three-eyed Śiva, riding on a bull —
tathaiveśaṁ pravakṣyāmi dhavalaṁ dhavalekṣaṇam
triśūlapāṇinaṁ devaṁ tryakṣaṁ vṛṣagataṁ prabhum.