The story regarding Katsuji KAWAMATA's naming of a car is correct, but the car in question was the SPL212, whilst the article says it was the SPL213. Their article in fact appears to be about the later series 310 and 311 models...
The true meaning of the 'Fair Lady' moniker which seems to go over most heads - and this goes for the musical production as well as GB Shaw's Pygmalion on which it was based - is that it is a corruption of "Mayfair Lady". Professor of Phonetics Dr. Henry Higgins was challenged to pass off cockney street urchin Eliza Doolittle as a society lady, and her mangling of the English language is the whole point.
When Eliza decried that she wanted the be a 'Mayfair Lady', it came out sounding like "My Fair Lady".
A little sports car from humble origins, aiming to punch above its weight and pass for something relatively exotic? I'd say 'Fair Lady' was quite a clever name with a hidden subtext that few actually *get*...