Potential Suggestions

Issue:

An unknown player has joined the Minecraft server.  Unknown how the player found the info to join however this player has joined.

Resolution:

Unknown player was removed permanently and added to a IP blacklist until further notice.

Information:

Minecraft server is using a non-standard port and DNS is not published or publicly announced.  As well as there are no mods/plugins that would broadcast the DNS of this Minecraft server (or at least that I am aware of).