If you search for “house under golden gate bridge” on Google, you will find a few other images of this house, even on the main search page, and all of the pages refer to it as a customs house, but none of them have any history or information. So if you then search for “customs house under golden gate bridge” the entire first page is populated with similar photos with no info. Deeper Google searches also return nothing. There is no Wikipedia entry for the house, and the entries for the bridge or the gate itself do not mention the house.
So I am unable to share any information. I do not know if it functions as a customs house, and if not (which I think likely) what it is used for now. That is Sausalito in the background, home of the fictional Cetacean Institute in Start Trek IV. In real life, Sausalito used to have a significant shipbuilding industry, but now not so much, I believe.