Shiva is called as Durdharsha because he is not suppressed by anyone. Acharya Bhaskar defines this name on the basis of story of Uttarkand section of Ramayanam—

कैलासे शिखरिणि पौलस्त्यप्रागल्भ्यं तृणसमतां प्राप।
एवं सत्यभिभवकारी कस्तस्मात्त्वं भवसि हि दुर्धर्षः॥

Total strength of Ravana turned meager like a straw while he faced Kailash mountain. If such is the fate of most vigorous Ravana, then who else can defeat you? You are known as Durdharsha because you are not defeated by anyone.
Once Ravana was passing near by Sharvana. At that time his airplane was obstructed in the midway. The reason for impediment was told by Nandi that – “Lord Shankar is resting at Mount Kailash and no one can transgress this path, therefore the speed of your plane is restricted.” Hearing this, he got very upset and he tried hard to uproot the Kailash mountain. Mother Parvati was very much frightened by the quaking of mountain. Then Lord Shankar pressed the mountain by a slight touch of his foot-thumb. Resultantly the pillar-like arms of Ravana were pinched under the mountain and he kept on crying and begging for pardon for thousands of years. Then finally Lord Shankar pardoned him. When Ravana was humiliated in this way, then who else can make a show of triumph before the Lord. Virbhadra who was born of Shankar, defeated Vishnu. Bhairva who came out from Shankar, smashed the head of Brahma. Then who may dare to stand still in front of direct valor of Lord Shankar?
Shiva is personification of knowledge. Shiva is named as Durdharsha because it is impossible to destroy or suppress the knowledge. Not getting allured by anyone in anyway during spiritual practices, is the true sense of worship of Durdharsha.