Why does my iPhone randomly Ding with no notification?

Check your notification settings to make sure certain sounds aren't set for certain notifications. You can receive notification sounds without receiving the banner or alert for them, so check that now by going to Settings > Notifications. More information here: Keep us updated.

Why does my phone keep randomly dinging?

A lot of the time, your iPhone keeps beeping for one of two reasons: Rogue notifications are making beeping sounds. An ad is playing an mp3 file which you are hearing through your iPhone's speaker. The ad is likely coming from an app you have open on your iPhone, or from a web page you were viewing in the Safari app.