Is there a name for the evolutionary loss of vestigial structures?
This phenomenon can be (and has been) described as regressive evolution (the loss of a phenotypic trait). There are several reasons why this occurs:


Neutral mutations which become fixed through genetic drift. 
Positive selection of regressive mutations that are beneficial. 
Pleiotropic antagonism: positive selection for one trait may have the consequence of disrupting another trait which isn't strongly selected for. 


The eye degeneration example you chose is a good one because it is well studied in cavefish (which evolved from sighted surface fish and have degenerate eyes). Normal eye development is under the control of the Pax6 transcription factor. Expression of another transcription factor, Shh, reduces Pax6 expression. Shh expression along the embryonic midline is responsible for splitting the eye field bilaterally. Overexpression of Shh in surface fish leads to eye degeneration and, indeed, it was found that cavefish have an expanded Shh expression pattern.

Cavefish have also undergone a behavioural shift to bottom feeding and have become less aggressive to focus more on finding food. As it happens, the expanded Shh expression also causes a widening of the jaw and amplification of taste buds, both of which aid in scooping and sampling the river bottom. Furthermore, increased Shh expression during brain development influences a decrease in aggressiveness and a shift to foraging behaviour.

This is an example of pleiotropic antagonism: positive selection for jaw enhancements and behavioural changes via expanded Shh expression, which increase fitness in cave environments, can explain why the eye degenerated.