I see, that makes sense. When you change any menu settings in Admin Menu Editor, it will apply the whole menu configuration – menu positions, permissions, etc – and not just the custom names. It can sometimes override changes made in other plugins. This depends on the order in which different plugins modify the admin menu during a page load.
In general, I would not recommend using multiple admin menu customization plugins at the same time. It can lead to conflicts like this one. If the plugins have different settings for the same menu items – for example, an item is visible in one plugin and hidden in another – one of the plugins will have to take precedence (because an item can’t be both visible and hidden), and the settings in the other plugin won’t work.
If you’d like to use Admin Menu Editor to edit the admin menu, please don’t use the admin menu settings in White Label CMS. Other White Label CMS settings should still work. Alternatively, if you prefer the menu configuration features of White Label CMS, please don’t edit the admin menu with AME.