It appears from the introductory dialogue between Rainsford and Whitney that Zaroff did not name the island but that it had had that name for many years before he even arrived there.
"What island is it?" Rainsford asked.
"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--"
The "old charts" could date back almost as far as the days when Spanish galleons were transporting cargoes of gold to Spain. The island could have gotten its name from sailors because it was known to have dangerous currents and reefs that could trap and sink ships, and because frequent storms drove ships onto its rocky shores. Zaroff has taken possession of the island and simply takes its traditional name along with it.
The fact that the sailors "have a curious dread of the place" is probably based on past and present. Strange things happened to ships in the distant past, and strange things have been reported as happening to ships in more recent times.
In any case, it seems likely that Zaroff did not name his island "Ship-Trap Island," although he is now using sophisticated traps to lure ships to destruction so that he can have a dependable supply of men to hunt. The fact that Zaroff did not name his island is indicated in the following excerpt:
The general's left eyelid fluttered down in a wink. "This island is called Ship Trap," he answered. "Sometimes an angry god of the high seas sends them to me. Sometimes, when Providence is not so kind, I help Providence a bit."
Zaroff would not say "is called" if he had named the island himself. It was called that before he ever heard of it. The island was the scene of many maritime disasters because "an angry god of the high seas" sent them to their destruction on this island with heavy storms and treacherous currents. The island had a bad reputation among sailors before Zaroff ever took possession.