It is a bit of a shame, IMO, that the concept of an always-on home computer has basically died out, or maybe never even really caught on. A sort of digital shadow of the house, it could run a home email server and do any home automation/content hosting. Anyway, I think it is unusual enough that it will need describing whatever he calls it, so no need to stress about the name. I’d call it the home computer, haha. Ever…
On a related note, I'm enjoying the Self-Host Weekly newsletter[0], which is full of random open source self-hosting products.