Based on quick research of the package name
com.mgoogle.android.gms, looks like it is a MicroG package used by YouTube Vanced.
The installation of this package is suggested by the official YouTube Vanced for non-root users if they want to add and login with a Google account.
Download & Install MicroG!
Download and install MicroG for YouTube Vanced in order to be able to connect your google account with YouTube.
If you don't install MicroG package, "add account" button will not work.
The renaming of the package is to prevent any conflicts with existing Google services.