Objects encapsulate data. This can include their name/id.

package Foo;

sub new {
   my ($class, $id) = @_;
   my $self = { id => $id };
   return bless $self, $class;
}

sub method {
   my ($self) = @_;
   ...
   if (...something went wrong...) {
      warn("$self->{id} rotted into a pile of mush\n");
   }
   ...
}
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use Foo;
my $one = Foo->new('one');
my $second = Foo->new('two');
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( If what you want to do is possible, it'll be hard, fragile and error prone. That's why I suggested this alternative. )