Canto 1 - Boyhood
Bāla-kāṇḍa
Chapter 18: The Advent of Rāma, Lakṣmaṇa, Bharata and Śatrughna
Text 1.18.23

वसिष्ठः परमप्रीतो नामानि कृतवांस्तदा॥

vasiṣṭhaḥ parama-prīto nāmāni kṛtavāṁs tadā

vasiṣṭhaḥ = Vasiṣṭha; parama-prītaḥ = greatly delighted; nāmāni = Their respective names; kṛtavān = gave the children; tadā = on that day.

Greatly delighted, Vasiṣṭha gave the children Their respective  names on that day.

Kṣatriyas are not allowed to name their children directly. According to the scriptures, they can do so only through their priest. That is what King Daśaratha did on the twelfth day from Rāma’s birth.