Being a patronymic name it represents anyone who is a descendant of the sage Babhru. The sage Girija of the Aitareya Brāhmaṇa and the sage Śaṅkha of Jaiminīya Upaniṣad Brāhmaṇa were Bābhravyas.
The sage Gālava, mentioned in the Mahābhārata, was also a Bābhravya. He was a great yogi and had organized the science of euphony of the Vedas (called Śikṣā).
The Skāndapurāṇa mentions a Bābhravya. Arjuna, the Pāṇḍava hero, during his pilgrimage, met Bābhravya and heard from him about the greatness of the sage Nārada.
One Bābhravya is said to have produced a condensed version of Kāma-śāstra (the Science of Erotics), originally written by Śvetaketu.