White labeling React Native apps
I found the project a project called white-label-app in github, I believe you can inspire yourself looking this project closer (and use them as boilerplate).
I'll try to use the majorajs, the idea of this package is "Manage white-label or skinned versions of your React Native app", sounds good for me.
You can use a combination of the React Native Bridge & product-flavors/targets to achieve what you want.
The process is extensive to setup, but once you have it setup it is very easy to add new white labelled apps to it.
I wrote a blog post that goes over every detail if you need a step by step guide.