I'm interested in a way to go from the package name (e.g.
com.android.providers.telephony) to its common name (Phone).
I'd like to know if there's ADB/shell command (from the phone), or any system/preinstalled app.
I know that a bunch of apps reveal both once you could pin the app in it. – In Android 4.x (tried with 4.2.2) you can even use the system app manager to confirm the package name once you found and selected the app via the common name.
aapt; and if yours does not, you can install it yourself (root required, though). Having that, a one-liner calling to ADB does the job for you. Details "over there" ;)