If you give yourself a boat with this command:

/give @a minecraft:acacia_boat[minecraft:rarity=epic]

The name is of the item is now pink.
However if you place the boat down, break it, and pick it up, the boat loses its rarity component. At least in its name it becomes white as if i didn't have the rarity component.

The same is true if you give yourself a block with rarity. If you break the block, then pick it up, it loses the rarity.
It can be reproduced with the custom_name component as well.