"simple symbol or graphic meant to represent something," 1937, probably a shortening of logogram "sign or character representing a word."
Entries linking to logo
logogram n.
"word-sign, sign or character representing a word," 1840, from logo- "word" + -gram. Generically, "any symbol representing graphically a product, idea, etc.," from 1966. The earliest use of the word (1820) is in the sense "logograph," but OED explains this as a substitute for logograph, "which in this sense is itself a mistake for logogriph," the old type of word-puzzle.