@chris3 I agree with you that this should be a feature (and actually I thought this was possible). Until that happens though, depending on which OS you're using, you'll find the list of DBMSs in one of these locations.
- Mac:
~/Library/Application Support/Neo4j Desktop/Application/persist/databases.json - Linux:
~/.config/Neo4j Desktop/Application/persist/databases.json - Windows:
%USERPROFILE%\.Neo4jDesktop\persist\databases.json
We don't recommend manually editing the persist files, but in this case, it should be fine if you just remove the entries that no longer exist in the filesystem.