The Board of Realtors has not always been the most diverse; however, it's equally plausible that the Castro was not yet in common usage as the neighborhood's name when the map was drawn
This is a small question that turns out to matter more than it looks, because MLS neighborhood names are not the names people actually use, and searches run on the wrong name miss homes.
The San Francisco MLS carves the city into ten numbered districts, each broken into named subdistricts. Those boundaries were drawn for the convenience of agents and appraisers, not to describe how anyone lives. They do not move when a neighborhood's identity changes, and they frequently disagree with Google Maps, with Zillow, and with what a seller would tell you at their own front door.
So a listing for a home most people would call the Castro may appear under Eureka Valley. A home in the Mission may show up under Inner Mission or Mission Dolores depending on the block. If you have set up an automated search by neighborhood name, you are relying on whichever boundaries that particular site chose, and nothing will tell you what you are missing.
The practical fix is to search by map area or by district rather than by neighborhood name, and to ask directly whether a search is skipping adjacent blocks. When a home seems mispriced relative to its neighbors, check first whether it has been filed under a subdistrict that pulls its comparable sales from a different set of streets.
On the naming question itself, I gave the same answer in 2016 that I would give today. Both explanations are plausible, and I do not think anyone can say with certainty which is right. Curbed SF has since shut down, so the copy linked here is an archived capture.
