I do according to documentation
module common created
res/values/public.xml
<resources>
<public name="app_name" type="string"/>
</resources>
Also tried
<resources>
<public/>
</resources>
res/values/strings.xml
<resources>
<string name="app_name">app_name</string>
<string name="app_name_2">app_name_2</string>
</resources>
Also tried without public.xml
res/values/strings.xml
<resources>
<public name="app_name" type="string"/>
<string name="app_name">app_name</string>
<string name="app_name_2">app_name_2</string>
</resources>
<resources>
<public />
<string name="app_name">app_name</string>
<string name="app_name_2">app_name_2</string>
</resources>
module app can use private resources
android.example.common.R.string.app_name_2