Canto 3 -
Araṇya-kāṇḍa
Chapter 3: Virādha Carries Rāma and Lakṣmaṇa
Text 3.3.6

पुत्रः किल जयस्याहं मम माता शतह्रदा।
विराध इति मामाहुः पृथिव्यां सर्वराक्षसाः॥

putraḥ kila jayasyāhaṁ mama mātā śatahradā
virādha iti mām āhuḥ pṛthivyāṁ sarva-rākṣasāḥ

putraḥ = am the son; kila = indeed; jayasya = of Jaya; aham = I; mama = my; mātā = mother; śatahradā = is Śatahradā; virādhaḥ iti = Virādha; mām = me; āhuḥ = call; pṛthivyām = on earth; sarva-rākṣasāḥ = all the rākṣasas.

Indeed, I am the son of Jaya. My mother is Śatahradā. All the rākṣasas on earth call me ‘Virādha.’

Virādha is a name appropriate for him because it means “one who can be overcome with only difficulty.” It is implied here that  this name was given to him by rākṣasas who belonged to his caste. The name was not given to him by his parents.

GLOSS. Sarva-rākṣasāḥ (“all the rākṣasas”) indicates that [Virādha] was popular in the world [of rākṣasas].