Ahem

use constant FOO => "a string";

sub constant_name {
  return (grep { $_[0] eq (\&{$_})->() } keys %constant::declared)[0]
          =~ /::(.*?)\z/;
}

print constant_name(FOO);
[download]

So it can be done, but don't do it like that, best listen to BrowserUk and use a hash map instead.
HTH

_________
broquaint