I found out that the way I hold my pencil is called the quad grasp, or at least it is by this page:

A quad grasp is similar to a tripod grasp except the pencil is held between the pads of the thumb, index and middle fingers, with the first knuckle of the ring finger supporting the pencil on the side.

Unfortunately, I couldn't find any other info on it, even with the search term "quad grasp."