This is speculation. Attempts to confirm this have so far been completely unrewarded by support or denial. I tried to ask Matt Johnson about this when I met him, but bad timing, and bad luck forbade.
The biography in the Sony web page says that the name, The The, was suggested by Keith Laws, the earliest collaborator with Johnson in The The. Where he got the idea for the name it does not say. In a book I read several years ago, it suggested that the name The The was essentially just selected because the punk surroundings in London was being frequented by group names which were simply repeated words. I am not sure whether the selection of the name was so simple, I would hope it had a more interesting history, but whatever.
The history of the name could relate to the American poet, Wallace Stevens (1879-1955). He was, even during his poetic successes, an insurance broker in Hartford, CT. His work is very similar to the work of The The. Exploring the darker elements of the human condition, relating the imperfections. It is in one particular Stevens poem that the similarities between become either eerily or explanatorially coincidental.