"Watch! Out there!" exclaimed the general, pointing into the night. Rainsford's eyes saw only blackness, and then, as the general pressed a button, far out to sea Rainsford saw the flash of lights.
The general chuckled. "They indicate a channel," he said, "where there's none; giant rocks with razor edges crouch like a sea monster with wide-open jaws. They can crush a ship as easily as I crush this nut." The reason the island is called Ship Trap is because that is exactly what it is. Rainsford had difficulty seeing the island in the dark and had he not fallen off of his yacht, he would have headed straight for that channel, and according to the quote above, his ship would have been utterly destroyed, leaving him (and we can assume many others before him) “trapped” on the island.
The name Ship Trap Island refers to what the island does to ships in the Caribbean. General Zaroff has a lighthouse on his island that attracts ships. This lighthouse makes it appear as if there is a safe passage through there. However, it lures ships in to the jagged rocks that break up the ships as they near the island. When the waters pull the ships in, their ships are wrecked and the men are trapped there. That is how Zaroff gets new prey every so often. The men become his "game" of hunting.
It's called Ship Trap Island because Zaroff needs men to hunt, so he literally causes ships to break up. He has installed lights to make it look as if a channel exists. In reality, the channel isn't there, but jagged rocks are that can tear a ship up, disabling it or causing it to sink. When a ship is forced to go to Zaroff's island, he has the sailors to pick from to hunt. As Zaroff says, however, the sailors don't usually provide much of a challenge for Zaroff, especially since he cheats. This is why he's so excited to get someone like Rainsford who is an expert hunter himself.
Zaroff has turned his island into a trap for ships, hence the name. When sailors are stranded due to following Zaroff's fake channel lights, he then uses them as game in a hunt. Ships are drawn by a series of lights (placed by Zaroff) into razor-sharp rocks, and hence, the inhabitants become shipwrecked prey for the general's deadly game.
Rainsford did not land on the island as a result of the lights, but rather, fell overboard while pursuing his pipe. It is coincidental that Rainsford, himself a skilled hunter, winds up on the island of a big-game hunter like Zaroff, but it serves to make the plot more intriguing.
It's called ship trap island because General Zoroff traps people on ships.