A purana story narrates an incident associated with the term Rudra. One day Brahma asked Shiva to create some beings as he was getting bored by creating , ordinary mortals. Then, Shiva created few immortal beings called as Rudras.
They were totally Eleven namely ::
Kapali.
Pingala
Bhima
Virupaksha
Vilohita
Ajesha
Shasana
Shasta
Shambu
Chanda and
Dhruva
So, they together are called as 11 Rudras.
Being the head of these immortal beings, Shiva is addressed as Rudra.
The hymns of Rig-Veda have lot of references to Shiva in the name of Rudra. They all portray Shiva as the highest God, a mighty archer , the most terrible form, the fire God and so on, these all express the fiery aspect of Shiva .
Shiva is the benign aspect of Shiva , where as the contrast Rudra is the fierce aspect of Shiva , thus bring the contrasting features of Shiva.
The literal meaning of Rudra is “ Roaring Storm / fire / fiery red .
The term Rudra focuses the fiery aspect of Shiva , which is destruction.
One para from Rudrashtakam ::
Prachannddam Prakrssttam Pragalbham Paresham
Akhannddam Ajam bhaanu_Koti Prakasham
Tryah_Shoola Nirmoolanam Shoola paannim
Bhajeham Bhavaani _ patim ,Bhaava_gamyam
The meaning is:: I bow to You Rudra , who is terrible , eminent amd extremely strong, who is the highest Lord. Who is ever Unborn and whole, and has the brightness of million Sun’s. Who has a trident in his hand, the three spikes of which uproots the bondages of the three gunas/qualities namely Tamas, Rajas and Sattva. I bow to you, the Husband of Devi Bhavaani , who can be attained by devotion.