As any Melville aficionado can tell you, the phrase "Ahab beckons" appears nowhere in Moby-Dick. It's one of Ray Bradbury's inspirations, added to the story when he wrote the screenplay for John Huston's 1956 Moby-Dick.
WARNING: SPOILERS AHEAD
In the 1956 film, the line "Ahab beckons" is spoken by Stubb (Harry Andrews), during the final chase of Moby Dick. Prior to this line, Ahab is knocked from his whaleboat, grabs the ropes streaming from Moby Dick to pull himself onto the whale's back, stabs the whale with a dangling harpoon while shouting two phrases taken verbatim from the book ("from hell's heart I stab at thee; for hate's sake I spit my last breath at thee"), and then becomes entangled in the ropes and drowns while bound to the whale's body. The three mates then see Moby Dick swim by, with Ahab's corpse plastered to his side, Ahab's dead arm flopping back and forth as the whale rolls. Hence, Ahab "beckons" to the sailors to follow him.
This makes for memorable cinema, but it bears little resemblance to what happens in the book. In the book, Fedallah (whom Bradbury excised in writing his version) is the one whose corpse the sailors (and Ahab) see lashed to Moby Dick's side. And there is no beckoning, even by Fedallah. His fate is instead tied by Ahab to a prophecy Fedallah had made ("Aye, Parsee! I see thee again," Ahab says. "Aye, and thou goest before; and this, THIS then is the hearse that thou didst promise."). What Bradbury apparently did was take bits of the Fedallah storyline and work it into his streamlined version, adding the visual touch of Ahab's waving arm.
Admittedly, an entirely faithful filming of Ahab's death would be quite underwhelming, since Ahab is jerked from this world in the blink of an eye ("voicelessly as Turkish mutes bowstring their victim, he was shot out of the boat, ere the crew knew he was gone").
END OF SPOILERS
So why would we title a blog devoted to the annual New Bedford Moby-Dick marathon with a movie line that has no analogue in the book itself? Gansevoort came up with the idea; I can't speak for his thinking. For myself, among other reasons, I think it reflects the gap between text and audience. Moby-Dick, more than other classics, demonstrates that a literary creation does not come with its own readership. Rather, it's at the mercy of the world it's launched into. Moby-Dick found a publisher, luckily, on the strength of Melville's earlier works, but it nearly sank like a stone on its first appearance. Some 50 years later, it was discovered and finally appreciated. It now remains a living classic, with real, non-academic readers, thanks partly to movies, the New Bedford Whaling Museum, and the museum's marathon.