Question

why concave mirror is called converging mirror

Answer 1

because iit converges the light rays to a point

Answer 2

If the object is placed infront of a concave mirror at infinty, beyond centre of curvature, at centre of curvature, between centre of curvature and focal point, at focal point it forms the real image of the object at focal point, between centre of curvature and focal point, at centre of curvature, beyond centre of curvature, at infinity respectively by converging the light rays from the object at respective positions. 

But if the object is placed between focal point and principal focus of a concave mirror it forms virtual image due to the diverging of light rays from object.

If the object is placed infront of the convex mirror it always diverges the light rays from object and forms virtual image.

so as the concave mirror converges the light rays in most of the cases it is called converging mirror and as the convex mirror diverges the light rays in all the cases it is called diverging mirror.