The NatWest and Ulster Bank brands are expected to remain unchanged, and the bank will continue to be called RBS on the stock exchange.
The Financial Times reported that the move "aims to break from the old strategy under former chief executive Fred Goodwin".
David Wheldon, chief marketing officer, said:
“We are no longer a global bank with global ambitions to be the biggest. We are now a UK and Ireland focused bank with a strong bank of brands and an ambition to be the best bank for customers.
“As part of our strategy to build a stronger, simpler, fairer bank we are dialling up our brands and directing our efforts to make each of our customer brands number one in their respective markets.”
RBS hopes to separate Williams & Glyn as a standalone challenger bank by 2017, but admitted last week that there is a "significant risk" the separation will not be achieved by 31 December 2017, and is currently exploring alternative means.
RBS says that "due to the complexities of Williams & Glyn's customer and product mix, the programme to create a cloned banking platform continues to be very challenging and the timetable to achieve separation is uncertain".
In Q1, Williams & Glyn new lending increased by 50% to £1.4 billion compared with Q1 2015. Notably, new mortgages were up 107% to £581 million, which RBS said were driven by a "more buoyant market, greater productivity and more competitive pricing".
When separation is complete, RBS says Williams & Glyn will be of the UK's largest banks with around a 5% business market share. It expects to have total assets of £20bn and customer deposits of £23.6bn.
