Did you purchase The Following DLC item individually? Do you own the Season Pass?

The name you see at Steam Store's description window is just a unified name for the whole product, i.e. Dying Light: The Following - Enhanced Edition. There can only be one name for one Steam product, so every user sees the same description and name for the same game. Not everybody is entitled to the same DLCs, though.

The most important indication of whether you own a DLC or not is your Steam Library window - not Steam Store:

Lastly, take a look at the ways of obtaining the Enhanced Edition and The Following DLC item itself, please: