Ugra is one of the Thousand and eight names of Śiva (Siva). Nīlakaṇṭha (Nilalohita), while explaining this name, says —utkarṣeṇa grasatītyugraḥ.
The verb-root ‘gras’ means to devotr. Mahādeva assumes a destructive form during the Pralaya (the mythical great doom), and devours the whole creation, so his name is Ugra. In Purāṇa (Purana), however, there is a different legend regarding this name of God Śiva. In the beginning of creation, Brahmā mentally conceptualised sage-sons like Sanaka, Sananda and others — who did not take part in procreation, and got involved in tapasyā. This made Brahmā angry. His wrathful energy issued out of the place between his two brows. From that energy, Mahādeva was born as Nīlalohita. The newborn started crying loudly, and  to pacify him, Brahmā  gave him eight names -leading to the conception of eight manifestations of  Śiva. The seventh among these names, is Ugra. As per Purāṇa, The Ugra-self of Nīlalohita Śiva is also his manifestation as yajñakartā (yajnakarta, one who performs the yajna) or yajamāna (one who gets the yajna performed). From this legend, too, the reason behind such naming of Ugra becomes evident.