Expected Mechanic : 
Naming Ender Chests shows  their name in GUI and keep their name when picked up after mining it again.

What happens : 
a) Breaking the ender chest does not yield in a named pick-up item. 
b) The inventory does not reflect the name change. 
b2) The wiki does state that this is a thing under it's Trivia Section
"Unlike chests, changes to an ender chest's name are not reflected in its inventory GUI."

What I think should be done :
a) Either disable renaming ender chests in an anvil
or
b) Have them reflect all name changes correctly
or
c) If the showing of the name in the gui is a wanted omission , then have the chest keep its name when breaking it

edit : 
After looking trough the rest of the submitted tickets, I have concluded mine stayed open because I address both the fact that the gui doesn't show the name change and the fact that the block doesn't keep it's name when mined again.

If I can elaborate on the issue : I'd just like to personalize the block so I can name it something and get emotionally attached to it. 
I do understand that the ender chest is not an actual tile entity that stores data/it's contents, but a mere container that reflects some player saved data, so it cannot save naming data to it's (nonexistent) save file. 

for the sake of consistency however, if you can rename all chests but one type, it would be nice to also be able to name that one type of chest.