It's the subtlety (and otherwise) of everything that goes with heritage. Changing the tail fins was a costly disaster. At the time, it was thought that because 70% or more of BA's customers were not British, it was a good idea to create a sense of recognition of that fact with those customers.
Also the name change could evolve into something more than juts a name change, but that's another side discussion.
If the idea was to change the name to reflect the non-english speaking passenger then perhaps choose something everyone understands.
It is doubtful that customers choose BA for any one single reason. Heritage however, will surely be reason enough for some people, as well as safety, seating, fares, frequency, routes, terminals, lounges and warts and all.