I can now answer my own question. I discovered this by connecting a keyboard and screen to the host and restarting …
If you change the name of your host in Stettings → System → Network, then HA automatically changes the domain to that name, with the ‘.local:8123’ suffix. So my system’s name is “AudreyHomeAssistant” and I can acess it through http://audreyhomeassistant.local:8123.
It would be nice if it were mentioned in the documentation on initial installation (in my case Generic x86-64 - Home Assistant) that “homeassistant.local:8123” is just the default name, and changes if you change the network name.
I guess this also anwers my next question: can you run two Home Assistants on one network? Presumably yes, if they have different network names (but I have not tried this yet).
I also notice that the host sets up an ‘observer’ on port :4357 of the same local domain. It’s just a singe web page that says the system is running. What is it used for?