Samsung s8 mobile phone receives short messages with no prompt tone and no prompt on the screen. What's going on here?

This is because the notification function is not enabled. The activation method is as follows:

First click the "Settings" icon on the phone desktop, as shown in the figure below.

2. After entering the phone setting interface, drop down the menu, and then select the "screen lock and security" option, as shown in the figure below.

Third, after entering the lock screen and security interface, turn on the switch in the "Notice" column, and there will be a new message reminder.

Fourth, you can also set whether the new message hides the content, as shown in the figure.