All the initial TriStar deliveries were short haul aircraft, and am fairly sure that as suggested above they did not carry individual names at first. But later in the 1970s with arrival of the -500s approaching, the company decided to name the entire fleet. Management hit on the idea of a staff competition for class and individual aircraft names with a prize for the best entry, probably in the form of free tickets.
Unfortunately for BA a group of staff, maybe T1 terminal staff, produced a spoof entry. Their proposal was the "British Airways Regrets" class, with individual names such as Technical Delay., Operational Reasons, Leased aircraft, Type Substitution, Unsuitable Weather (etc). None of this would have mattered too much, except the joke came to the attention of the LHR freebie newspaper Skyport which ,lacking the editorial control which BA imposed on its own newspaper, published the story on its front page much to everyone's amusement. Except presumably that of BA management, because the joke was close to the bone.
The winning entry was the English Roses class, and these names adorned the L1011 fleet until the change to the Landor livery.