Those make no sense and should just be branded as Southern services.
It seems the 387s can't easily be changed from one TOC/brand to another. GTR has solved the problem on the GN services by now making trains say 'the service to' with no name at all.
Ideally, they'd not only get rid of the premium but dual-brand like GA on the Stansted Express services. Then you could just run Southern trains, but call them Gatwick Express similar to how FCC had the Cambridge Cruiser (still a FCC service).
GatEx is just a mess and needs sorting, but it clearly won't when it's a great moneyspinner.