@313103, you're getting two very different sorts of thing confused.
Essex Thameside, South Western and Greater Anglia are rail franchises. The right to operate services in these areas is tendered by the DfT to the highest bidder.
Essex Thameside is currently operated by C2C Limited trading as C2C; South Western (which includes services from Ryde to Shanklin, as well as services from Waterloo) by Stagecoach South Western Trains Ltd trading as South West Trains, and Greater Anglia by London Eastern Railway Ltd trading as National Express East Anglia.
All contractual arrangements with the DfT are with these limited companies, which keep separate accounts and are separately managed (the MD of London Eastern is Andrew Chivers; the MD of C2C is Julian Drury).
As it happens, C2C Limited and London Eastern Railway Limited are both owned by National Express Group plc. NEG sells central services (ie office space, HR, marketing departments, etc) to both companies. But these have to be provided on a transparent, arm's length basis so that if either company lost its franchise, an incoming franchisee could easily take over - precisely as happened when the Silverlink franchise ended and was split into LO and part of LM.