The origin of the name, as with most coastline features in this series of curiously named locales, is nautical. In 1585 an English explorer called Sir Richard Grenville was sailing to Roanoke Island when his ship became trapped in a bay behind the cape. There was some concern the ship would run aground and wreck, hence the name Cape Fear. According to George Stewart, author of Names On the Land : A Historical Account of Place-Naming In the United States, it is one of the five oldest surviving place names in the USA.
A fun side note; panic grass grows near Cape Fear. That's almost as good as the trail leading to Mt Defiance in Oregon starting at Starvation Creek. Also, for flavor and a bit of retroactive justification for this series, I present to you an excerpt from George Stewart's book:
"The poetry of a name may spring from three sources. There is the romantic appeal of sonorous sound and sensuous connotation, evoked by the strange and the unknown. People who cherish a name chiefly for such reasons do not usually like to have it explained or translated. For them, the poetry is not enhanced, but vanishes, when they learn that Atchafalaya means 'long river.'A second source of poetry is in the historical association of the places which lie close to men's hearts-in names like Virginia, Plymouth, and Concord, the shrines on our long pilgrimage. But again we must not err in thinking history something of the far past. The poetic suggestion of a name may be of recent growth-the glitter of Hollywood, the grim power of Chicago.A third source of poetry is largely the opposite of the first. It is the poetic suggestion which springs from the inherent meaning, even though the actual event of the naming may be unknown. The United States seems particularly rich in such names — Sweet-water, Marked Tree, Lone Pine, Gunsight Hills. In this lies the charm of Cape Fear, Cape Flattery, Cape Disappointment, and Cape Foulweather; of Broken Sword, Broken Straw, and Broken Bow. These are the names which seem to have stories of life and death behind them — Roaring Run, Deadman Creek, Massacre Lake, Rabbit Hole Spring."
Sources:
https://en.wikipedia.org/wiki/Cape_Fear_(1991_film)
https://en.wikipedia.org/wiki/Cape_Fear_(headland)
Names on the land : a historical account of place-naming in the United States - by Stewart, George Rippey, 1967






