Once Upon a Time ... In Hollywood was released recently. One of its promotional taglines was "The Ninth Film From Quentin Tarantino", which sounded both like a bit of ego of stroking and a recognition of just how well known the writer-director has become. Even many people who haven't seen his films know his name and often the titles of some of his films and have an idea of what they tend to be like (notably, violent). That's fame.
Let me put it this way: Avengers: Endgame is the highest-grossing movie of all time but it's fair to say its directors, Joe Russo and Anthony Russo, are not all that well known outside the circles of comic-book and superhero-film fans.
However, Tarantino has probably got some way to go before surpassing the household-name ubiqitous-recognition status of some other filmmakers, past and present.
Steven Spielberg, for example, is also a very widely recognised name although unlike Tarantino, it's harder to pin him down to a specific kind of movie: genres he's directed movies in include science fiction (Close Encounters of the Third King, E.T. The Extra-Terrestrial, Jurassic Park), historical drama (Schindler's List, Lincoln, Bridge of Spies) and adventure (the Indiana Jones films). But his name, for most people, would be connected to at least one movie.
Likewise, Spielberg's sometime collaborator, George Lucas, whose role in creating the Star Wars films is well known (even if he didn't direct all of them: directors Irvin Kershner and Richard Marquand, who respectively directed The Empire Strikes Back and Return of the Jedi would elicit blank looks from all but devotees).
As far as the idea of auteurism goes - where some directors are regarded as the "author" of their films - I'm a little sceptical: while Tarantino, who writes as well as directs his movies which have specifically recognisable elements, has some claim to this status, all films are, ultimately, collaborative endeavours.
Cecil B. DeMille was recognised as a maker of spectacles such as The Ten Commandments in his day and was one of the few directors who could fairly be called household names in an era when information was less easy to come by than it is now. But how well known is he to younger generations? Other, more feted filmmakers of the era were, and are, probably less widely familiar, like John Ford, the only director to win four Oscars
Arguably, there are two long-deceased filmmakers who are the best-known, most enduring household names. One is the Master of Suspense, Alfred Hitchcock, many of whose films including The Birds are still widely recognised, referenced and watched today. He still needed collaborators, though: Bernard Herrmann's scores for several films were important, especially Psycho, as Hitchcock acknowledged, contributed greatly to the film's impact.
The other is Walt Disney, whose studio still bears his name and whose achievements in animation as producer and creative force, including Snow White and the Seven Dwarfs, are still appreciated today.
Like Hitchcock, he was a shrewd multimedia figure: both had TV shows in which they appeared, making their visages as well as their names familiar and helping cement them into the culture. Whatever works.