Udgra was one of the names of Śiva Mahādeva (Siva Mahadeva). Commentator Nīlkaṇtha (Nilkantha) explained the meaning of the name of Śiva (Siva) as Udagra-
Udagraḥ (Udagrah) Urjitarūpaḥ (Urjitarupah)|
Urjita means Tejaswī (Tejaswi or full of power). Lord Śiva (Siva) was often imagined as Agni or fire. Fire has the power to burn and as Śiva (Siva) was the epitome of fire, he was named as Udagra.
Īśwara Puruṣa (Iswara Purusa or the lord as male power) was imagined as the center of all the Śakti (Sakti) or power of this earth. This universal manifestation of Īswara (Iswara or God) depicted him more powerful than Agni or fire and the sun. Even the power of the sun or the fire was a small fraction of the powerful epitome of Īswara (Iswara or God). In the Bhagvadgītā (Bhagvadgita), this powerful manifestation of the Parameśwara (Parameswara or the ultimate lord) was depicted in a way that when the thousand suns would enlighten the sky, the power of this light then can be compared with this vast universal manifestation of the power of the Parameśwara (Parameswara or the ultimate lord)-
Divi Sūryasahasrasya (Suryasahasrasya) bhaved yugapaduththitā (yugapaduththita)|
Yadi bhāḥ (bhah) sadṛśī (sadrisi) sā (sa) syadbhāsastasya (syadbhasatstasya) mahāṁanaḥ (mahatmanah)||

For this grand powerful manifestation of lord Śiva (Siva), he was famous as Udagra. As he was Udagra, he was also Rudradeva.