Apparently they were invented by a guy called Florian Wiesmann who called his brakes "Wies-brakes", which sounds a lot like "V brakes" to an English speaker.
In 1991 he made this brake:
Apart from the centred brake cable attachment, that's very much like a modern V brake. By 1996 he had something you'd look at and swear it was a slightly fancy-looking V brake clone, and that seems to be the year Shimano introduced the V brake.
In 1991 Ben Capron was also selling his Marinovative V brake that also looks just like a modern V brake. IRD also began selling their Widget brake. So "who invented the V brake" is a complex question and it may well have been a parallel discovery.
Mombat say on a link I got from Google cache because the page doesn't appear to exist now:
[IRD] Developed the Widget brake, because they needed a brake that could mount to the rear swing arm. This and the Marinovative Brake are the progenitor to today's V-brakes.