Shankar is called as Ugra because he holds very fierce form to destroy the demoniac forces. The relevance of blessing power is esteemed, when it is flavored with restraining power. Shiva is very merciful, but sometime demons try to exploit his mercy. So he has to assume a fierce form. He strengthens Bhasmasura by granting him special boons, and at a particular time he defeats him by dint of the same strength. This terrorism of Shiva is the base of communism of democratic powers in the society. By his trident weapon Shiva personally kills the demons like Tripurasura, Gajasura and Andhakasura etc.

Veda also adore Shiva by uttering this name— Namo Ugraya. According to Abhinav Shankaracharya eminence is indicated by the word ‘Ugra’. Shiva is named Ugra as he possess eminent qualities. The demoniac qualities like lust, greed and anger, which are elaborated in Bhagvad Gita and which hinder the path of knowledge, they are conquered by Lord Shankar, so he is called Ugra.

Actually the means to attain Shiva is denoted here. The mind can not become one with Shiva without seizing the contrary factors. Therefore slaying of powerful evils is expected. Shiva alone is the destroyer of them, being fixed in the renounced state of mind. As the sun enters by his rays in the magnifying glass and burns the objects into flames, similarly Shiva enters in the mind and destroys the ignorance.

Maheshwara has directly revealed the secret of his fierce form in Mahabharata. There are two concepts in the world namely Som and Agni. One is hot, while other is cold. The coolness is present in Vishnu, while Lord Ugra sustains all the planets by his fiery deity named Agnibhava. This form is terrible with furious eyes, and decorated with weapons like trident etc. Such form of Lord Shiva is called Ugra.

According to Acharya Bhaskar— O Lord! You pervade this material world. You are transcendental to this world. You are the presiding personality of Vayu (air element) and you are residing in the form of Ugreshwar Lingam at Kanhal region, so you are known as Ugra.

उच्यस्यन्तर्निखिलजनानामुद्रच्छस्यप्यथ जगदूर्ध्वम्।
प्रव्यक्तः सन् कनखललिंगे वायोरन्तर्वससि तदुग्रः॥

Below is the description of Shiva Purana which states the fierceness of Maheshwar—

बहिरन्तर्जगद्विश्वं बिभर्ति स्पन्दते स्वयम्।
उग्र इत्युच्यते सद्भीरूपमुग्रस्य सत्प्रभो॥

Great scholars call you ‘Ugra’ because you maintain the creation internally and externally, and you pulsate in the creation yourself. Cultivation of divine qualities in the self by elimination of demoniac qualities, is the true form of worship of Ugra.