SK53
The convention in OSM is to map what is visible on the outside, and that has been NatWest for at least 20 years. Not least because a customer of NatWest will search for that term not the (outdated) older form. It does appear that the holding company is still called National Westminster Bank plc, but it in turn is part of NatWest Group in RBS plc. 

Also note that expanding initials for retail brands is dangerously prone to errors (HMV are not His Master's Voice, ASDA are not Associated Dairies, TSB is not Trustee Savings Bank etc).

It is also wise to follow the most widely used convention: NatWest: https://taginfo.openstreetmap.org/search?q=natwest#values; National Westminster: https://taginfo.openstreetmap.org/search?q=National+Westminster#values