When using storage as text component for custom_name, item_name or lore of an item, it will show nothing.

For example:

/data modify storage test test set value 123

/tellraw @s {"storage":"test","nbt":"test"}

/give @s diamond[custom_name='\{"storage":"test","nbt":"test"}']

The second command will output 123 in chat, but the third one will give you a diamond with an empty string, where in theory you should get a diamond with custom name "123".