$0 is Lvaluable so you could anticipate any changes to it. Simplistically you could just:

BEGIN{$0 = "foo"}

Or if you want to watch it's state just tie the thing:

package Progname;
use Carp;

sub TIESCALAR {    
    my $class = shift;
    my $newname = shift;
    return bless \$newname, $class;
}

sub FETCH {
    my $self = shift;
    carp "The program name is being accessed.\n";
    return $$self;
}

sub STORE {
    my $self = shift;
    my $attempted = shift;
    carp "An attempt is being made to change the program name to \"$at
+tempted\".\n";
    
}

1;
[download]

And then:

use Progname;
tie $0, 'Progname', "NewProgramName";
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