UNC shares using domain name not computer name

How can I point a shared folder to the domain name instead of pointing to a specific computer?

Example:
I have a folder called "public", now it is shared on a domain named "mydomain" on a computer called "server".
So when I need to access this folder I write \\server\public

But, I would like to have the UNC \\mydomain\public.
note the difference, I refer to the domain name not a computer name in the domain.

I would like not to use DFS...

Thank you for any help.