There's the media itself (like your TV shows), there's the actual Plex Media Server that manages your media, and then there are
the Plex client applications you access the server from via your Apple TV, your iPhone, or other devices.
Not exact matches
Unless you've changed the name within the
client application itself, the name is usually the hostname of the device it is on (the
Plex client on my home office computer is identified as J - Office, for example).
But if you have multiple
Plex clients on your home network and you want to take advantage of
Plex's built - in support for sending media from control
applications, like
Plex for iOS or the
Plex Media Server web dashboard, you'll run into a problem really quickly.