Amogha is one of the names of Śiva-Mahādeva (Siva-Mahadeva). Nīlakaṇṭha (Nilakantha), the commentator, while explaining the meaning of the name, writes — ‘amoghaḥ naiṣphalyarahitaḥ‘.
In Upaniṣad (Upanishad), it is said that one who, after knowing the Brahman properly, prays or practices asceticism in order to attain that Brahman, is blessed with fulfilment of all his desires. No desire of him remains unattended or futile —
sa ya āśāṃ brahmetyupaste āśasya sarve kāmāḥ samriddhyantamoghā hāsyāśiṣo bhavanti yāvadāśāyā gataṃ tatrāsya yathākāmacāro bhavati, ya āśāṃ brahmetyupāste.
God Śiva is the manifested self of that absolute Brahman who fulfills all fruits of desire.
However, the name of Śiva can also be explained thus — benevolent to his devotees, He keeps no desire of them unfulfilled. His devotees get every bliss they want, by His grace. So He is known as Amogha.