Parrots lose their Name Tag upon dismounting a player's shoulder

The bug

Named parrots lose their name when mounting a player's shoulder (can be seen when looking at the ShoulderEntity NBT data) and therefore have lost it when dismounting again.

How to reproduce

1. Spawn a parrot and tame it
2. Name the parrot
3. Walk into the parrot to make it mount your shoulder
4. Jump to make it dismount