From Klee & Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory (MAA, 1991), p. 251:
"D. Champernowne, while an undergraduate at Cambridge University, proved that 0.123456789101112131415... is normal in base 10"
The citation there is to the following short paper: "The construction of decimals normal in the scale of ten," J. London Math. Soc. 8 (1933) 254-260.
Not having read the paper nor knowing much at all about our friend Champernowne, I will still surmise that the term "normal" was introduced with this 1933 paper, the choice of a young mathematician who was probably ignorant of the theory of the normal distribution.