How to find out the package name of an Android app, without ADB nor installing apps
There are multiple approaches to that – depending on what you have access to. I'll include those not working for you as they might work for others:


Most obvious: use an app inspector (link goes to my corresponding app list). Won't work for you as you cannot install any app.
Not that obvious, but with helpful side effect: install ClassyShark3xodus from F-Droid. Not only shows the package name but also the trackers contained in apps. Again, needs installing an app.
Another one with helpful side effects: installing Helium Backup and inspecting the backup file name. Doesn't work for you either, unfortunately.
Native method: Open in Play Store, ideally in the web page. Find the package name in the URL's id parameter. If in app, use the developer's name to list all apps made by them: https://play.google.com/store/apps/developer?id=&lt;url+encoded+name&gt;.


If the app is not available in any of the app stores available on the device (often happens with vendor specific pre-installed apps), you're out of luck: you cannot even extract the APK from your friend's device if (s)he doesn't let you install an APK extractor or enable ADB (with ADB, you could e.g. use Adebar's getapk script to extract all or specific apps).