I like the idea from choroba, but I would perhaps do it a bit differently. The OP doesn't specify what to do if the rename cannot happen. I would just "die" in that case with an error message. I would only process .mp4 files that match the pattern, but again that is up to the OP to decide how to handle an .mp4 file that doesn't match the pattern.

use strict;
use warnings;

foreach my $file ('Jane Doe & John Doe - 124 - How to Invest.mp4',
                  'Jane Smith & John Smith - 100 - Stocks.mp4',
                  'Jane Black & John Black - 90 - Bonds.mp4',
                  'Jane Black & John Black - 120 - Bonds2Invest.mp4',
                  'Jane Black & John Black - 123 - Bonds 2 Invest.mp4'
+,
                  )
{
   if ( (my $num) = $file =~ / (\d+) - [\w ]+.mp4$/ )
   {
      #rename $file, "[Books] $num.mp4" or die "Cannot rename $file to
+ $num.mp4 - probable cause: duplicate number: $!";
      print "$num.mp4\n";
   }  
}
__END__
124.mp4
100.mp4
90.mp4
120.mp4
123.mp4
[download]