On his initial voyage Dias never actually landed anywhere near Cape Town. For thirteen days his ship was caught in a raging storm, after which he laid anchor at Mossel Bay (a few hunderd kilometers up our east coast). When Dias eventually turned back and found Cape Town, he named it Cabo das Tormentas, the Cape of Storms. King John II of Portugal later renamed it to Cabo da Boa Esperança, meaning Cape of Good Hope, because it opened up a sea trade route to India and the rest of Asia.
Note: This really really big propeller can be found outside the Mediterranean Shipping Company's offices in Martin Hammerschlag Way.