The short answer is that it was the last name on a piece of paper after Rachael and I had taken turns to cross off the ones we didn’t like.

Here’s the longer answer from our website:
It’s a double quote, from Mike Leigh’s film Naked, which in turn quotes the Book of Revelation. On the Day of Judgment the Seven Seals are broken, and seven angels blow their trumpets, and “when the Third Angel blows hers, wormwood falls from the sky and poisons a third of all the water and a third of all the land”, and many people die. And the Russian translation of ‘wormwood’ is Chernobyl.

Apparently some people believe that the Chernobyl disaster was the third seal being broken on the ‘Day’ of Judgement. This isn’t a religious thing for us. In 1995 we were pretty interested in a lot of that apocalypse culture stuff – the installation we made in 1996 called Barcode made reference to all barcodes containing three sixes. We came up with a shortlist of possible names, and in the end we chose Third Angel as a name because we liked the sound of it – and we had to get the poster for Testcard to the printers.
(http://www.thirdangel.co.uk/about.php)

Best wishes

Alex