>>93648433Your uncle is largely correct.
Ever since DC bought the right to reprint the old Fawcett Comics back in the early 1970s, they've also been looking for other ways to market him. This led to three series - two live action and one cartoon - over the following decade.
These were the The Kid Super Power Hour with Shazam! (animated, 1981), Shazam! (live action, 1974-1977, later the Shazam!/Isis Hour) and The Secrets of Isis (live action, 1975-1977), which was about a Wonder Woman-like character whose powers, like those of Shazam, came from an ancient magical source (in this case the Egyptian goddess Isis, explaining the name). The two live-action shows frequently crossed over, and Isis was eventually adopted into DC Comics as well.
Because DC quickly discovered that they didn't own and would never own the trademark Captain Marvel (which Marvel Comics had held since 1967, some five years before DC tried to acquire it, and a decade and a half after first trading as Marvel Comics), Shazam was the name they chose to market the character under - and the Shazam! and Shazam! Power Hour shows were the biggest exposure the long-forgotten character had been given in decades, which is why your uncle even remembers the character at all, and remembers him as Shazam!
Although the cartoon and live shows did use the Captain Marvel name, this was never prominently featured on any marketing material or merchandise, at least not more prominently than Shazam! (which in the case of the live show was an acronym invoking the elders who granted his powers; the cartoon was closer to the early comic books, unlike DC's 1970s offering which changed to be more like the live show, and pulled some shitty tricks like naming the city Fawcett City, after the competitor DC forced out of business for publishing Captain Marvel originally.) The cartoon was never that popular and cancelled after 12 episodes.
The official switch, as other anons have pointed out, was much more recent.