First of all, other NFL teams have names that reference states rather than cities. So this type of [broader geographic] name would not be unheard of.
Secondly, the Golden State title is inclusive. That is crucial. The gesture will welcome a lot of [understandably alienated, angry] San Diego folks back into the fold. That name might also be inclusive enough to bring some Northern & Central Californians into the fold. It is just a clever idea. It will expand the Charger fan base rather than shrink it and that is key.
Thirdly, the "Golden State" moniker already has some cachet, what with the success of the Golden State Warriors.
Fourthly, the name sounds good to the ear.
Fifthly, the team can still remain in LA, retaining its current fans in the LA area.
Sixthly, the LA market is pretty saturated with professional teams, and established teams at that. The Chargers would do well to expand the reach of the franchise beyond LA.
Lastly, there is already gold in the jersey, so it really fits quite well.
I really don’t think there is any downside to it. Frankly, it should be done as soon as possible.
The Chargers are not the most popular franchise in California or anywhere for that matter, in part due to some very questionable decisions made in recent years by the upper brass of the organization. Changing the name to the Golden State Chargers could constitute a real overture to potential fans in the region, and could really work as a kind of semi-rebranding. It could also do something psychologically for the squad. The only other "golden state" team in the world is a tremendous team in their respective sport. Nobody, and I mean nobody, associates "gold" with anything poor, ignoble, or unsuccessful.
Branding is important, and the Chargers brand is somewhat sickly. Changing the name to the Golden State Chargers could really change a lot on that front.