The Birds is a pretty straightforward title. You've got a movie about bird attacks here. You don't call it The Chipmunks.
The title does reiterate something important, though, which is that those birds are the stars. Melanie and Mitch, Bodega Bay itself—none of them get top billing. It's not called The Playboy Bachelor or That Blonde From the City. Tippi Hedren and the other actors have to say their lines and furrow their brows and scream at the right moment, but they're not the main event. When you sit down to watch The Birds, you're there to see those birds.