In Brihadaranyaka Upanishad 3.9.4 , Rishi Sakalya (शाकल्य ) ask to the Rishi Yagnavalkya (याज्ञवल्क्य) , “Who are Rudras ?”
Rishi Yagnavalkya replies :
शेमे पुरुषे प्राणा आत्मैकादशः; ते यदास्माच्छरीरान्मर्त्यादुत्क्रामन्त्यथ रोदयन्ति; तद्यद्रोदयन्ति तस्माद्रुद्रा इति ॥
The ten organs in the human body, with the mind as the eleventh. When they depart from this mortal body, they make (one’s relatives) weep. Because they then make them weep, therefore they are called Rudras,’
Mahabharata mention their number and names as following :
मृगव्याधश्च सर्पश्च निर्ऋतिश्च महायशाः ।
अजैकपादहिर्बुध्न्यः पिनाकी च परंतपः ॥ 2॥
दहनोऽथेश्वरश्चैव कपाली च महाद्युतिः।
स्थाणुर्भवश्च भगवान् रुद्रा एकादश स्मृताः ॥ 3॥ – Mahabahata Adi Parva 66.2-3
मृगव्याध, सर्प, महायशस्वी निर्ऋति, अजैकपाद, अहिर्बुध्न्य, शत्रुसंतापन पिनाकी, दहन, ईश्वर, परम कान्तिमान् कपाली- स्थाणु और भगवान् भव ये ग्यारह रुद्र माने गये हैं
Mrgavadha, Sarpa, Nirriti, Ajaikapad, AhiBudhnya, Pinaki, Dahana, Ishvara, Kapali, Sthanu and Bhaga are eleven Rudras.
Story of birth of eleven Rudras
This story is mentioned in Shiva Mahapurana – Satarudra samhita – chapter 18
Once, the devatas went to sage Kashyapa after being defeated by the demons. They complained to him about the misdeeds of the demons, who also happened to be their step brothers. Sage Kashyapa hearing their prayers decided to protect the them and commenced penance to please lord Shiva.
Lord Shiva became very pleased by his penance and appeared before him. Kashyapa then requested Lord Shiva to take birth as his son and destroy the demons. Lord Shiva agrees to the same.
Lord Shiva, later on took birth as eleven Rudras from the womb of his wife Surabhi.
These eleven Rudras fought battles with the demons and defeated them. The deities were relieved after the death of the demons. They worshipped these eleven Rudras to express their gratitude and indebtedness.