Finally, after two months, I managed to put us on the map!
Before, using Google Maps for local organizations, people in our area had only two options: Unitarian Church (yes, their profile was sometimes directly shown for the keywords like "humanist") and Humanist Association.
Now, even if you search for "humanist fellowship" on the main serch engine page, we come first under the map - we are locally discoverable. After establishing our Google My Business presence, registering by paper mail with Google, tweaking service areas, adding cards and stuff like that, it started to look acceptable.
Google put me through a lot, but now all can see us, our area (SD County) correctly, links, etc.
If you have a google account, please review HFSD (link on the bottom left, on the panel by the map on desktop, scroll down on mobile).
HFSD on the map: