That is a good idea. They could take a string or a symbol with a default string value.
The variables shell-command-buffer-name(-async) could be declared as defcustom instead of defconst.

On Fri, Dec 22, 2023 at 2:18 PM Eli Zaretskii <eliz@gnu.org> wrote:
> From: Nafiz Islam <nafiz.islam1001@gmail.com>
> Date: Fri, 22 Dec 2023 12:31:24 -0500
>
> The buffer name for the shell-command or async-shell-command would be much more useful if they
> were given the name of the command being executed.
>
> I started working a bit on a patch for that, but it's just code changes right now. Here's a preview of
> what I mean.

Instead of removing the default name, why not add one more possible
value to async-shell-command-buffer, which will do what you want?
Then users who are interested in this behavior could customize
async-shell-command-buffer to that new value.

Thanks.