FirebaseApp name [DEFAULT] already exists

It's not clear what your goal is. If you simply want to modify ("overwrite") the default FirebaseApp that is created by FirebaseInitProvider, I don't think that is possible. The documentation you cited is a little misleading in that it suggests it is possible. I think the documentation is intended to describe how the default app can be initialized when it has not already been created, for example in a secondary process.

You can use FirebaseApp.initializeApp() to create another app object. You need to use the method that accepts a parameter for the app name:

    FirebaseOptions firebaseOptions = new FirebaseOptions.Builder()
          .setDatabaseUrl("[DATABASE_URL]")
          .setApiKey("API_KEY")
          .setApplicationId("PROJECT_ID").build();

    FirebaseApp myApp = FirebaseApp.initializeApp(getApplicationContext(),firebaseOptions,
        "MyAppName");

You can then use the created FirebaseApp to get an instance of FirebaseDatabase, FirebaseStorage, FirebaseAuth, FirebaseCrash, or FirebaseInstanceId. For example:

FirebaseDatabase database = FirebaseDatabase.getInstance(myApp);

In an app's main process, I don't think there is a simple way to disable the initialization processing done by FirebaseInitProvider. If you want to override the configuration parameters that normally come from google-services.json, you can probably create your own XML file for the parameters using the information in the documentation for the Google Services Plugin. It states:

If your Android project has some configuration that prevents you from using the google-services plugin, you can safely recreate the XML files manually using these values

I don't know how simple or maintainable that is.

Use this

FirebaseOptions options = new FirebaseOptions.Builder()
    .setApiKey(apiKey)
    .setApplicationId(appId)
    .setDatabaseUrl(firebaseBaseUrl)
    .build();

boolean hasBeenInitialized=false;
List<FirebaseApp> firebaseApps = FirebaseApp.getApps(mContext);
for(FirebaseApp app : firebaseApps){
    if(app.getName().equals(FirebaseApp.DEFAULT_APP_NAME)){
        hasBeenInitialized=true;
        finestayApp = app;
    }
}

if(!hasBeenInitialized) {
    finestayApp = FirebaseApp.initializeApp(mContext, options);
}