The Taittirya Upanishad makes up the seventh, eighth, and ninth Vallis (sections) of the Taittirya Aranyaka of the Yajur Veda. The last of these three Vallis is called the Bhrigu Valli, and this how its first chapter begins:
Bhrigu Vâruni went to his father Varuna, saying: "Sir, teach me Brahman." He told him this, viz. Food, breath, the eye, the ear, mind, speech. Then he said again to him: "That from whence these beings are born, that by which, when born, they live, that into which they enter at their death, try to know that. That is Brahman."
Now Bhrigu is a very famous sage; as I discuss in this question, he is the father of Sukracharya guru of the Asuras, and as I discuss in this answer and this answer, he was the one who cursed Brahma that he could never be worshipped, and cursed Shiva that he could only be worshipped in Linga form.
But my question is, why is he given the surname "Varuni" in this passage, and why is Varuna the ocean god called "his father"? Bhrigu is usually described a son of Brahma, not Varuna. Could this be similar to how the sages Vashishta and Agastya have the surname Maitravaruni, even though they were originally sons of Brahma, because they were reborn as sons of Mitra (god of friendship) and Varuna?