I'm going to give an alternative explanation, though it's speculative.
Govia wish to minimise the disruption to services south of the river and are running trains in their relevant paths when possible, with their relevant descriptors, south of Blackfriars.
This obviously has the benefit of having less effect on customers south of the river, but the cynic in me wonders if this arrangement is due to it being economically beneficial for GoVia. lf for example a train runs as a Bedford to Brighton service, with stops north of the river cancelled, could it be that GoVia incur lower penalties? Of course they may well claim the money back from NR but that's another matter entirely.
Last night during the chaos, they certainly kept changing trains headcodes on the fly (3 times on one train in the space of 10 minutes). My immediate thought was that is was due to it being more beneficial to run it as another service closer to booked time.
As I said, speculation.