You could probably put the server behind Tor for additional privacy. Mint to relay communication would still be needed afaik understand it.

The mint is running on a server, but it's not accessible via IP. You communicate with the mint using its npubs via nostr relays. afaiui. 🫂

You can't communicate with a server without having its address. You might be able to discover the address via another route that isn't traditional DNS (pigeon comes to mind. Or Nostr), but you ultimately need the IP to connect to it.