One circular route that thoroughly confuses me is the Cannon Street (CST) to Cannon Street via Sidcup and Woolwich Arsenal, and the reverse route via Woolwich Arsenal and Sidcup.
NRE is very inconsistent as to how this service is shown, it appears to change dependent on time and day.
e.g. the 13:40 today from Cannon Street today is displayed as destination "London Cannon Street (Circular Route) via Sidcup and Woolwich Arsenal" at both Cannon Street and London Bridge outbound.
The same service at 13:49 from New Cross is displayed as destination "Woolwich Arsenal", however if you click to see the detailed list of stops, you get to see all of the circular route.
At Crayford, the destination changes to "London Cannon Street via Woolwich Arsenal and Greenwich"
At Erith, the destination changes again to "London Cannon Street via Greenwich"
and finally at Westcombe Park it becomes the "London Cannon Street" service.
At all points, clicking on the detail shows the full circular route from CST to CST.
However the service one hour later, leaving at 14:40 is presented differently. From New Cross to New Eltham it is "London Cannon Street via Sidcup and Woolwich Arsenal". From Sidcup to Erith it is "London Cannon Street via Woolwich Arsenal and Greenwich", and from Belvedere to Charlton it is "London Cannon Street via Greenwich.
Half hour later, and the service terminates at Woolwich Arsenal for stations from New Cross to Sidcup, but this time the detailed list of stops only shows stations from CST to Woolwich Arsenal, it doesn't look like a circular route at all. However from Sidcup onwards, it shows as destination CST, and the detail once again shows CST to CST circular.
So in the above cases, it appears random as to where the service is going. My experience at the stations is that the local displays and announcements are not in sync with NRE. And the front of the train typically will say "Slade Green" and not change until it gets there.
The reverse route is just as random, often showing as terminating at Hither Green, sometimes as a through circular route, and again the detailed list of stops changes along the route.