It can get its name by using one of the forms of caller(). Try this:

foo();

sub foo {
  my @callinfo = caller(0);
  print "i am $callinfo[3]\n";
}
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Not reliably. Here's code that breaks dws' example. I've never had the need for the feature you describe, however. (I could also walk the symbol tables until I found the right CV, but that's even worse. :)

my $sub;

BEGIN
{
    $sub = sub {
        my ($called) = (caller(0))[3];
        warn "Called as <$called>\n";
    };

    *{ bar } = $sub;
}

my $b = \&bar;
$sub->();
*{ foo } = $sub;
foo();
bar();
$b->();
*{ baz } = $b;
baz();
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