The Golden Gate Bridge is named for the narrow entrance between the Pacific Ocean and the San Francisco bay known as the Golden Gate Strait.
So the Golden Gate bridge isn't named for the bridge itself but for the narrow entrance between that Ocean and San Francisco bay.
The Golden Gait strait was named by the explorer and the U.S. Army officer John C. Frémont, who marveled at its beauty in the year 1846 which was two years before the discovery of the gold in California.