The crater Ley is attached to the northeastern rim of Von Neumann, and is somewhat overlain by the outer rampart.

There is some slumping along the inner wall to the northwest where the rim makes its closest approach to Campbell, and the narrow terrain between these two craters is rugged and irregular.

There is a small range of ridges running from the south to the northern edge of the floor, and the ground is more irregular in the eastern half.

There are no significant impacts within the crater interior and the sides are generally unworn.

Prior to formal naming by the IAU in 1970,[1] Von Neumann was called Crater 58.