TileEntity block items don't preserve their item's custom name

1) Get a mob head, chest, or any other block item that has a tile entity associated with it
2) Re-name it in the anvil
3) Place it
4) Break it

You'll notice that it didn't save the name.

No this is not "impossible because they are blocks placed into the world". All TileEntities are capable of storing such information.

I'm pretty sure this used to work, and it got broken or something.