We call the convex mirror as a diverging mirror because the light rays when get reflected from the mirror appear to be diverging from a point behind the mirror.
The concave mirror reflects the parallel rays of light in such a way that after reflection, all the rays spread out. Therefore we can say that the rays of light are diverging. Therefore, the convex mirror is called a diverging mirror.

Convex mirror as diverging mirror

Some of the learners also asked:
How will be the reflecting surface of a spherical mirror?