Kevin Bier, chairman-emeritus of the TWAIN Working Group and the one of the original co-author/editors of TWAIN 1.0, chose the name TWAIN after reading letters by Mark Twain. It was unofficially considered to mean "toolkit without an important name."
The word "twain" is an archaic form meaning "two". It appears in Kipling's "The Ballad of East and West" - "...and never the twain shall meet...", reflecting the difficulty, at the time, of connecting scanners and personal computers. It was up-cased to TWAIN to make it more distinctive. This led people to believe it was an acronym, and then to a contest to come up with an expansion. None were selected, but the entry "Technology Without An Interesting Name" continues to haunt the standard.