In my custom Blocks (Hybrid Blocks) is in the advanced-Panel the option “BLOCK NAME” visible. But the value is not saved nor reflected in the structure panel.
This is still an experimental feature, which might change eventually:
If it would be added down the line it might loose support / change meta name with the core update and etc, this as I understand it would not be viable to implement it right now.
Yep, whilst they have decided to have this feature & where its should be fully controllable in 6.5 - for now we just need to wait for 26th of March for the stable release.