Mojo::DOM makes such things fairly trivial. Consider the following:

#!/usr/bin/perl
use strict;
use warnings;
use feature 'say';

use Mojo::DOM;

my $html = '<h2>2.1. Match Literal Text</h2>
<h2>2.2. Match Nonprintable Characters</h2>
<h2>2.3. Match One of Many Characters</h2>';

my $dom = Mojo::DOM->new( $html );

#for each hr
foreach my $hr ( $dom->find('h2')->each ){
  # grab the text
  my $class = $hr->text;
  # remove x.x.
  $class =~ s/\-?\d+\.\d+\. //g;
  # update the DOM
  $hr->attr('class' => $class );
}
# display updated DOM 
say $dom;
[download]

Prints:

<h2 class="Match Literal Text">2.1. Match Literal Text</h2>
<h2 class="Match Nonprintable Characters">2.2. Match Nonprintable Char
+acters</h2>
<h2 class="Match One of Many Characters">2.3. Match One of Many Charac
+ters</h2>
[download]

Please let me know if you have any questions.