This looks correct to me. I think it should be testable with docker up on one's laptop starting from a clean checkout, after changing the database name settings, and seeing if you get a working server.

This didn’t work; see discussion.

TL;DR: I don’t think we should be expected to support customizing the database name for our own database. The custom database name feature is for connecting to a separate centrally or externally managed PostgreSQL instance where the administrator decides what the name is.