Try this. Go to settings then search reset settings. This will only reset settings to default except the security,language and account settings. Personal setting and settings of downloaded apps won't be affected. This worked for me.
This is ridiculous. I've only had my S8 for 5 days, so when I see this thread was started a year ago I assume there's a solution among the 23 pages of replies. Never assume...I get no notifications at all and none of the posted "solutions" work. I was adamant that I was staying with the S series phones...now I'm not so sure.
This worked for me on my Galaxy s8...
Settings -> Notifications -> scroll down and click on the Messages app -> New Messages -> Importance. This is where I noticed Low and Medium show 'no sound'. This must have changed after the last update. I changed it to High and now I get all notifications for text messages.
Go to notifications>Advanced(top right corner)>Messages app>New messages>then under sound I had a number, so I clicked on it and picked the notifications tone I wanted and backed out of all that and it fixed the problem. I hope this helps.