Why does my iPhone keep making a dinging noise?

Have you worked through all the app settings in Notifications to see if turning them off one by one stops the noise? Checked to see if there are any alarms or timers set, perhaps in a third-party app? Restarted your iPhone?

Regards.

It may have to do with the apps you have installed. Such as Facebook's separate Messenger app.

While I do have notifications on for Messenger, I always keep the volume of my iPad all the way down to mute. And yet, when I get something in Messenger, the iPad audibly dings anyway.

I don't know how they do it, but Messenger can somehow bypass your volume setting.