It isn't definite but I'd just make something like this the server name:
"Server Name [PRIVATE]" or "Server name [NO LOGINS]"
Another option would be to warn of a boot in your server's MOTD. Give them a few minutes or so and give them a friendly kick in the behind. Most people are fine with it as I had to do it on my server before. People don't have a problem with it if you warn them.
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