How to stop players joining my Minecraft PC server under my name?

You could try running your server with online mode (which means you might have to purchase a copy of Minecraft) so that players have to authenticate (proof that they're themself) themselves before they can join.

Otherwise a plugin like this (one that prevents play until you separately authenticate yourself after logging in) that prevents others from reusing a taken name also works.

Otherwise, what you'll have to live with it, and ban yourself (to stop others from using your name) and deop yourself whenever you log out.

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To set your server to online mode, go to your server.properties file and edit:

online-mode=false

to:

online-mode=true

Either that or change your account's password and secure your email address.

Instead of banning the username, try banning the IP that the player is logging onto your server through. You'll see it in the server log.

Unless they can somehow change their IP, which we hope is not the case, they should have a harder time getting onto your server.