Display Name of entity or block in open Inventory does not update

The name of an entity or block in the top left of its open inventory does not update (if changed) while the player has the inventory open. Only by closing and reopening the inventory, the new name is displayed.

How to recreate with two players:

Player 1 opens inventory of Horse/Donkey/Camel/Lama.
Player 2 uses renamed Name Tag on this Entity
Player 1 does NOT observe change of name. Only by closing the inventory and reopening the new name is displayed.

How to recreate with commands for entities:

Summon entity with an inventory, that the player can open. (Horse/Donkey/Camel/Lama/Chest Minecart/Chest Boat…)
Setup impulse command block with a delay (multiple repeaters) with this command:

/data merge entity @e[type=the entity you use,limit=1,sort=nearest] {CustomName:"TEST 123"}

Press Button and quickly open the inventory of the entity. Observe how the Name does NOT change. Only by closing the inventory and reopening the new name is displayed.

How to recreate with commands for block entities:

Setup impulse command block with a delay (multiple repeaters) with this command:

/data merge block ~ ~1 ~ {CustomName:"TEST 123"}

Place block entity on top of command block with an inventory, that the player can open. (Chest/Hopper/Dispenser/Crafter/Brewing Stand…)

Press Button and quickly open the inventory of the block. Observe how the Name does NOT change. Only by closing the inventory and reopening the new name is displayed.