Just because I learned the flip-flop recently:

#!/usr/bin/perl -n
print if (/NAME/../SYNOPSIS/);

# then:    man ls | this_script.pl
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OR maybe you have other plans for the text...

#!/usr/bin/perl

$cmd = shift;
open MAN, "man - $cmd |";

while (<MAN>) {
   $section = $_     if /^[ A-Z]+$/;
       
   push @lines, $_ 
     if $section =~ /NAME|DESCRIPTION/;
}

do_something_else_with(@lines);
  # perhaps get rid of the page headers/footers
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