I have been watching the Barking live cam, which has these trains running past it. When I go into the train information, the operator of record is listed as Arriva Rail London, though the trains have the correct London Overground livery.
To expand on G92’s comment, London Overground is a public brand controlled by the DFT, which is ran under contract by private companies. London Busses for example are all red and have the ‘Busses’ branding, but have various underlying operators such as Arriva/Abellio/Go Ahead/Stagecoach etc. There were also talks of doing something similar with the national rail network.