I think the A() has at least has the advantage of being 100% clear to whoever reads the code (no one will think this might still be a bareword).
A , "Value" won't match the style of other key/pair values (or the standard notation), and ,=> looks enough like a typo (or even syntax error if you're not familiar with perl) that someone will be tempted to correct it. I agree that (A) is a beautiful solution :)

There are of course many silly alternatives, like %hash = reverse ("Value" => A, "Value" => B);, or using $::{A}->$*, but the only other correct solution I can think of is prepending the package name.

use strict;
use warnings;
use Data::Dump qw( pp );

use constant A => "One";
use constant B => "Two";
package Consts
{
  use constant C => "Three";
}

pp {
      main::A   => 1,
      ::B       => 2,
      Consts::C => 3,
    };



__DATA__
{ One => 1, Three => 3, Two => 2 }
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And having your constants in a specific namespace may be a good idea in the first place.