On the server page, in the Name card, you give your server a new name (field “What you call this server”) and confirm with the tick. It appears in the client area, on invoices and in emails. Only the owner can rename a server.
Name in the game
The name players see in the server browser is something else. Depending on the game, you set it:
- under Startup variables (e.g. “Server name” or
SERVER_NAME), - in the Settings tab (Minecraft: MOTD, 7 Days to Die: name),
- or in the configuration file under Files.
The article for your game tells you which applies. Restart the server afterwards.