if you just want to replace the first occurance of a name, then use the following

my %new_names;

$file =~ s{^\s+description\s\K(\w\w\w\w)(?=-\w+-\w+;)}{ 
    my $name = $1;

    if (!$new_names{$name}) {
        $name = $new_names{$name} = my_rand();
    }
    
    $name
}gme;
[download]

Or if you want to replace all occurances of a name with the new name, then the following would work:

my %new_names;

$file =~ s{^\s+description\s\K(\w\w\w\w)(?=-\w+-\w+;)}{ 
    $new_names{$1} //= my_rand();
}gme;
[download]

Note: since the suffix appears to not be relevant, I added it to the positive look ahead assertion.