It depends.
@fiatjaf made a push for making relays front-and-center and insisted that this needed to be nostr direction and paid out bounties for things like 'seen on' information.
IMHO for general microblogging relays are invisible. For DMs too. Nobody cares about the relays when you are just conversing deep down in some thread.
But for other apps (relay-centric chat, browing relay-specific feeds) the relays have to be known to the user. This is like a web browser: the URL is not invisible, the user goes to the URL they want to see.
So it very much depends on the nostr app in question.
In the context of this thread though, relays cannot be invisible. People have to choose their relays, often making decisions like "should I pay for service here", "is this relay reputable", "what does my son recomend as the best relay".
