How to reproduce
Give yourself a named zombie head using
/give @s zombie_head{display:{Name:"{\"text\":\"item\"}"}}
Place it down and break it
→ ❌ Observe that the name is lost, and it is again "zombie head"Give yourself a named banner using
/give @s white_banner{display:{Name:"{\"text\":\"item\"}"}}
Place it down and break it
→ ✔ Observe that the name is kept, and is still "item"
Related issues
Attachments
Comments

Relates to MC-91006.
Confirmed for 1.13.1-pre1
Confirmed for 1.13.1

Confirmed for 19w50a

Skulls and heads have no reason to save it, unlike the blocks who do, all blocks who do retain their name have it either show in the gui, or are banners and can be seen on maps; no other block entities retain their name because they cannot be seen either way.
This is by design, and the report is a feature/change request.
Can confirm in 21w06a.
Can confirm in 1.16.5 and 21w10a. Video attached.
I'd consider this to be a duplicate of MC-174496 since this ticket has an assigned Mojang Priority and is more actively updated.
Resolving forward to MC-174496.