Clarification Re: Customizing Grub menus

[Richard Owlett <rowlett@cloud85.net>]

On 12/08/2021 06:33 AM, Richard Owlett wrote:
> I have a machine set aside for experimenting with different 
> configurations of Debian. The default Grub2 menu will display OS(with 
> version) and partition designation in /dev/sdXY format.
>
> I give all partitions descriptive labels.
> I want the Grub menu to display OS and the partition label.
> I want it to update appropriately after using update-grub.
>
> Is there an appropriate tool?
> TIA

Received answers did not seem to answer my question.
That suggests a unclear question ;}

On my test system partition labels are:
  /dev/sda7	full-10
  /dev/sda9	minimal-11

Default Grub menu after install of buster reads:
  Debian GNU/Linux 10 (buster) (on /dev/sda7)

I wish it to read:
  Debian GNU/Linux 10 (buster) (full-10)

After installing bullseye and running update-grub without any manual 
intervention, I wish appropriate lines to read:
  Debian GNU/Linux 10 (buster) (full-10)
  Debian GNU/Linux 10 (bullseye) (minimal-11)

Possible?
If so, how?
TIA