To confirm that your phone's ringtone has indeed been changed, you can check the Phone ringtone under the Sounds & vibration menu.
If you wish to set a ringtone to a specific contact, as your notification tone, or even as your alarm ringtone, you can select those options from the same menu. You'll see a toast notification at the bottom of the screen telling you the ringtone has been applied. (Image credit: Namerah Saud Fatmi / Android Central)