Credit for the game that bears his name is due to to Borel. It appears in a 1921 paper in French. An English translation (by Leonard Savage) may be found in a 1953 Econometrica.
The first appearance in print of a version of the game with Colonel Blotto’s name attached is, I believe, in the The Weekend Puzzle Book by Caliban (June 1924). Caliban was the pen name of Hubert Phillips one time head of Economics at the University of Bristol and a puzzle contributor to The New Statesman.
Blotto itself is a slang word for inebriation. It does not, apparently, derive from the word `blot’, meaning to absorb liquid. One account credits a French manufacturer of delivery tricycles (Blotto Freres, see the picture) that were infamous for their instability. This inspired Laurel and Hardy to title one of their movies Blotto. In it they get blotto on cold tea, thinking it whiskey.