K comes from the Greek word kilo which means a thousand. The Greeks would likewise show million as M, short for Mega. So if we stay consistent with the Greek abbreviations, then billion would be shown as a letter G (Giga). Think of your computer expressing bytes of memory as kilobyte, megabyte, or gigabyte.

k, eleventh letter of the alphabet. It corresponds to the Semitic kaph and the Greek kappa (Κ). It has changed its shape less perhaps than any other letter in the history of the alphabet. The Semitic form may derive from an earlier sign representing a bent hand.