I am using BungeeCord and if someone changes his Minecraft name his rank on the spigot servers is gone but the rank on the bungeecord stays.

Is the bungeecord option turned on in the spigot.yml on your spigot settings? If this is false, the spigot server may get the wrong UUID information.

This is likely a configuration error.

I agree with @SimonOrJ - most likely a config issue.

Please follow the steps outlined here.
https://github.com/lucko/LuckPerms/wiki/Network-Installation

:)