Someone wrote to say that Golden Gate Park in San Francisco is part of the system known officially as the Golden Gate National Recreational Area, which stretches up the coast north of the Golden Gate itself. You could take this as an explanation as to why a park which isn't anywhere near the Golden Gate is called Golden Gate Park. I'd say it points toward a possible explanation... the phrase "Golden Gate" must have had powerful name recognition back when these parks were being set up. Much easier to get congress to fork over money for a great American symbol like the Golden Gate, even if you're talking about something like Point Reyes, which is way out of town.

Funny, it never occured to me that Golden Gate Park was under federal control in any way. In recent years we've had a bunch of local referendum that imply it's under the city's control, for example on subjects like "should they build a parking garage in the middle of the park". (This actually passed, but just barely.)