Notifications causing screen waking

I recently got a new MacBook Pro (2019 model). With this computer, if the displays are sleeping (I often have an external monitor attached via USB-C dock), they will wake up for a few seconds when a notification comes in, and then they go back into power-saving mode. My previous MBP (late 2013 model) did not have this problem. I call it a problem as the computer is in my bedroom, and the momentary flash of light is waking me up sometimes at night. How can I stop this from happening? (Both Macs are running 10.14.6)

You can turn on Do Not Disturb ("DND") mode to prevent distractions or notifications during specific timeframes.

Source:

Schedule Do Not Disturb

1. On your Mac, choose Apple menu > System Preferences or open "System Preferences" directly from the icon.
2. Click "Notifications".
3. Select "Do Not Disturb" at the top of the sidebar.

You can stop notifications during a time period, when your Mac is in sleep (useful if you sleep near your Mac) by checking the "When the display is sleeping" box.

If you want to receive call notifications even when Do Not Disturb is on, select the call checkboxes.