The god faded and the word did not. Bhaga receives no independent temple cult, acquires no iconography, and after the Vedic period he survives mainly in the Aditya lists and in the astronomical tradition, which assigns him the lunar mansion Purva Phalguni. His vocabulary, however, went everywhere. Bhagya is fortune, good or bad. Bhagavan, formed from the same stem, means the one who possesses the shares, and it becomes the ordinary respectful title for a divine being: Bhagavan Vishnu, Bhagavan Buddha, and the Bhagavad Gita, the song of the possessor of shares. Nothing in that usage refers to the Aditya, but all of it descends from the idea he personified.
The name also has securely attested Indo-European relatives, and they run in the same direction. Old Persian and Avestan baga means god, and the Slavic word for god, bogu in Old Church Slavonic, comes from the same root. In several branches of the family the word for the one who distributes shares became the general word for a divinity. That is a rare and rather clean piece of comparative evidence about what an early Indo-European community thought a god primarily did.
Read back into the Rigveda, that makes Bhaga less marginal than his small number of hymns suggests. He is not a minor god who happened to be called Portion. He is a survival of an older way of naming the divine, sitting inside a collection that had already moved on to gods of storm and war.