I used react-native init MyApp to initialise a new React Native app.
This created among others an Android project with the package com.myapp.
If you are using Android Studio-
changing com.myapp to com.mycompany.myapp
create a new package hierarchy com.mycompany.myapp under android/app/src/main/java
Copy all classes from com.myapp to com.mycompany.myapp using Android studio GUI
Android studio will take care of putting suitable package name for all copied classes. This is useful if you have some custom modules and don't want to manually replace in all the .java files.
Update android/app/src/main/AndroidManifest.xml and android/app/build.gradle (replace com.myapp to com.mycompany.myapp
Sync the project (gradle build)