Did it ever do this?
"Badges" on icons to indicate a new message are not a standard Android feature. Some third party launchers, such as Nova or Apex, can do this, but if you just have the stock launcher(*) then no, you won't have that feature.
If you did have it and now it's gone you've most likely changed launcher, changed a setting or removed the add-on that provided this service to the launcher.
(*) A "launcher" is the app that provides your desktops, dock and app drawer. Every phone comes with one, and many people may not be aware that the desktop is a separate app rather than an integral part of the operating system, but this also means that you can find alternative launcher apps in the Play Store. The two I named can both do what you want, provided you use them in place of the built-in launcher and install a small add-on app to handle the notifications (called TeslaUnread for Nova, Apex Notifier for Apex).