Renaming a react-native app manually is simple.
The app name displayed on the iPhone home screen comes from the CFBundleDisplayName (or "Bundle display_name_") as the human-readable string in Xcode) entry of your iOS app's info.plist.
The app name on android comes from AndroidManifest.xml. Check the label attribute of<application>
This value is typically referenced as a named variable, defined in strings.xml