There are no item name labels shown when using the chest interface with a controller. In MCPE 1.1 the item name was displayed when an item was moved, but in 1.2 the item name is never displayed.
The old way was better, but not particularly good still. The item name should be displayed when it is highlighted, as is done in the inventory and crafting interfaces already. You shouldn't need to move the item in order to find out what it is.
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I just noticed that this issue only occurs when moving a stack of items (using the Y button on my controller). If I move items one at a time then there is a pop-up with the item name.
I can't confirm this, since i don't have a controller, but on my windows 10 (non-beta) dispensers don't display "Dispenser" in their UI. No problem with droppers, hoppers and chests though
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