The Golden Gate bridge gets it's name after the Golden Gate Strait which is a narrow 300 feet deep turbulent stretch of water that is below the Golden Gate Bridge which connects San Francisco Bay on the east to the Pacific Ocean which is on the West.
The Golden Gate Suspension Bridge Spans the Opening of the San Francisco Bay and onto the Pacific Ocean.
When the Golden Gate Bridge was being built the steel had a red primer on it.
The Red Primer was shown to be a close enough good color for the surrounding area and they then chose the color of orange vermilion called international orange to paint the bridge with over the primer.
The Orange Vermilion paint worked well with the current primer on the bridges steel so they went with that color to paint the bridge.