How to use flavors with different app names in Android studio?

Remove the app_name string from your existing strings.xml file, then you can do this:

productFlavors {
    originalFlavour{
        resValue "string", "app_name", "Original Flavor Name"
    }

    freeFlavour{
        resValue "string", "app_name", "Free Flavor Name"
    }
}

Then the existing reference to @string/app_name in your manifest will refer to a generated string resource, which is based on the flavor selected.

Note that if you specify a label for your launch Activity (by defining the android:label xml tag in the <activity> element), that value will be used in many user-visible places rather than your application’s label. To overcome this for your case, you can just remove the label from your <activity> element altogether. See https://stackoverflow.com/a/13200774/2911458 for more details on this distinction.