I do like the hash for clean and obvious enumeration, but I hate the explicit hash and typing key names more than once, so I tend to hide both declaration and invocation in subs:

#!/usr/bin/perl -s
use strict;
use warnings;
use 5.014;

our $h;
sub callback; our %CALLBACKS;

# Callback functions ---------------------------------------

callback first => sub {
    my $z = shift;
    print "in first_callback, z=$z\n";
    return 1;
};

callback last => sub {
    my $z = shift;
    print "in last_callback, z=$z\n";
    return 2;
};

# Implementation of dispatch table -------------------------
# (You need to write this code)

sub callback {
    my ($name, $cb) = @_;
    $CALLBACKS{$name} = $cb;
}

sub invoker {
    my ($name, $z) = @_;
    return -1 unless exists($CALLBACKS{$name});
    $CALLBACKS{$name}->($z);
}

sub help {
    say "Available callbacks: @{[ sort keys %CALLBACKS ]}";
}

# Main program for testing ---------------------------------

exit help() if $h;

for my $name ( "first", "last", "fred" ) {
    my $rc = invoker( $name, $name . '-arg' );
    print "$name: rc=$rc\n";
}
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Results:

$ perl /tmp/1203952.pl -h
Available callbacks: first last
$ perl /tmp/1203952.pl
in first_callback, z=first-arg
first: rc=1
in last_callback, z=last-arg
last: rc=2
fred: rc=-1
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