What was the name of the large island?

"Ship-Trap Island" is the name of the large island in this story.

We discover this name in the third paragraph of the story, as Rainsford and Whitney are standing on the yacht, viewing the island off in the distance:

"The old charts call it 'Ship-Trap Island," Whitney replied. "A suggestive name, isn't it? Sailors have a curious dread of the place. I don't know why. Some superstition--"

As Rainsford and Whitney ride past the island, they discuss it a bit more:

"The place has a reputation--a bad one."

"Cannibals?" suggested Rainsford.

"Hardly. Even cannibals wouldn't live in such a God-forsaken place. But it's gotten into sailor lore, somehow. Didn't you notice that the crew's nerves seemed a bit jumpy today?"

With these characters being on a ship, and with the distant island portrayed as so creepy and named "Ship-Trap Island," we definitely get the feeling that at least one of these characters will encounter the island: either to be trapped by it, or perhaps to be trapped on it.

As you read the rest of the story, finding out about the dangerous hunting game taking place on the island, you start to realize how appropriate the island's name really is. Though the island is named for the literal line of rocks surrounding it, which tends to sink (and therefore trap) any ships that approach it, you also notice that Zaroff, the resident of the island, has set up his own trap for ships: a system of lights that look like a safe channel but actually lead straight into the dangerous rocks. In this way, both nature and man have made the island an effective trap for ships.