This feature suggestion covers this scenario; the initial request was to be able to record shows not in the guide, but it gets expanded upon in the comments:
As of right now, you’re going to have problems with these different airings, as you’ve discovered. If each airing truly has the same name, Plex Media Server will just consider these as different airings of the same show. (In my market, the all the networks name their airings differently, including the time. For example, “WYFF News 4 at 5pm” and “WYFF News 4 at 5:30pm” and so on. So they can all be recorded independently.)
If you could find and utilize XMLTV guide data (instead of Plex’s native guide data) you could likely write a script to give each airing a unique name adding, for example, an “at H:MM” to differentiate them. Where you’d obtain that XMLTV guide data I’m not sure. Schedules Direct provides such data, but I don’t think their service terms allow for usage with Plex.