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](https://dev.bukkit.org/projects/authme-reloaded) (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`](https://minecraft.wiki/w/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.