All arrow types lose their name/NBT data when shot and picked up

The bug

Arrows lose their name and NBT data when shot and picked up.

How to reproduce

1. Obtain a bow and give yourself an arrow with a custom name:

   /give @s minecraft:arrow{display:{Name:'{"text":"MC-1981"}'}}

2. Shoot the arrow on the ground using the bow
3. Pick up the arrow
   The arrow no longer has a custom name

Expected behavior

Arrows would not lose their NBT data when shot and picked up.

Note

Other issues previously tracked in this ticket are now reported in MC-91005, MC-91006 and MC-91007. See this discussion for details.