Why is it called dynamic range?

Multiple frames are captured and extra information (as in more lighting) is added to some frames and reduced in others. The frames are then combined into one to amplify the bright and dark colors. This gives you a high range of saturation which can be changed, so that's why the HDR stands for High Dynamic Range.

It's not the difference, it's the ratio.

A ratio does not have a fixed 'bottom' or 'top', therefore is dynamic rather than static.

Ref: Wikipedia - Dynamic Range

Seemingly-constant illumination in fact represents a mixture of high-frequency waves. If the intensity is low enough, and one exposes a piece of film, these waves will cause a sequence of randomly-distributed changes to the states of the crystals in the emulsion. While some kinds of detection apparatus may seem to regard light as a steady state, what actually happens within the apparatus is that light will knock something in the apparatus out of its rest state, then the apparatus will reset it, then light will knock it again, etc. The processes associated with light are generally so fast that, by the law of large numbers, they appear uniform, but underneath that apparent uniformity things are in fact constantly changing.

Is the answer more simple?

Static range suggests a fixed scale regardless of external influence.

Dynamic range suggests the scale is affected by external influence.

So the range at say, 12 noon on a bright sunny day would have a wider difference than 12 noon on a cold dull grey day.

The scale (say 0-99) would still represent the contrast/ratio between darkest and lightest, but the differences between the individual increments of the scale would be dynamic, based on physical lighting conditions.