Maybe you could play with AUTOLOAD() instead of aliases and caller. AUTOLOAD is made to do this sort of thing.

use strict;
use warnings;

sub AUTOLOAD {
    my $called = ( split /::/, $main::AUTOLOAD )[-1];
    my %recognized;
    @recognized{'this', 'that', 'those'} = ();
    exists $recognized{$called}
        or die "I don't know how to $called.\n";
    print "I was called as $called\n";
}

this();
that();
those();
woops();
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