What to do when I get no notifications for incoming messages on my Galaxy S8?

I’m not 100% sure if you’re using the pre-installed messaging app, and therefore can’t give you the exact steps here. Basically, there are two things you should check.
1. Go to the messaging app settings, and make sure you’ve turned on the notifications.
2. Then, go to the device settings > Notifications, find the messaging app and make sure it’s turned on here.

If it’s just a particular contact that you don’t get the notifications, follow these steps:

1.open the Messages app.
2. Tap that particular contact’s conversation.
3. Tap the Menu button in the upper right corner, and check if you’ve accidentally disabled the Notification button at the bottom of the extended menu.

Thanks for your help. Indeed, I’ve accidentally turned off the notifications of my good friend.