The etymology of the theonym "Rudra" is somewhat uncertain. It is usually derived from the root "rud-" which means "to cry, howl." 
According to this etymology, the name Rudra has been translated as "the Roarer". 
An alternate etymology suggested by Prof. Pischel derives "Rudra" ("the Red, the Brilliant") from a lost root "rud-", "to be red" or "to be ruddy", or according to Grassman, "to shine". 
Stella Kramrisch notes a different etymology connected with the adjectival form "raudra", which means wild, of "rudra" nature, and translates the name "Rudra" as "the Wild One" or "the Fierce God". R. K. Sharma follows this alternate etymology and translates the name as "Terrible" in his glossary for the Shiva Sahasranama. 

The commentator suggests six possible derivations for "rudra". However, another reference states that Sayana suggested ten derivations. 

The adjective "shivam" in the sense of "propitious" or "kind" is applied to the name Rudra in RV 10.92.9. According to Gavin Flood, "Shiva" used as a name or title (Sanskrit "", "the kindly/auspicious one") occurs only in the late Vedic "Katha Aranyaka" Axel Michaels says "Rudra" was called "Shiva" for the first time in the "Śvetāśvatara Upanishad". 

Rudra is called "The Archer" (Sanskrit: "") and the arrow is an essential attribute of Rudra. This name appears in the Shiva Sahasranama, and R. K. Sharma notes that it is used as a name of Shiva often in later languages. The word is derived from the Sanskrit root "-" which means "to injure" or "to kill" and Sharma uses that general sense in his interpretive translation of the name as "One who can kill the forces of darkness". The names ("Bowman") and ("Archer", literally "Armed with arrows in his hands") also refer to archery.

In other contexts the word "rudra" can simply mean "the number eleven".

The word "rudraksha" (Sanskrit: ' = "rudra" + ' "eye"), or "eye of Rudra", is used as a name both for the berry of the Rudraksha tree, and a name for a string of the prayer beads made from those seeds.

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