To add onto what the others have said, "golden" refers to "The Golden State" (California). The state is called that because of the 1840's gold rush.
The Golden refers to the mouth of San Francisco Bay, not the bridge. In other words, it is the Bridge Over the Golden Gate. That entrance to the Bay was called the Golden Gate before the bridge was there.
The world-renowned bridge is named for the Golden Gate Strait, the narrow, turbulent, 300-foot-deep stretch of water below the bridge that links the Pacific Ocean on the west to San Francisco Bay on the east
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