Let me rewrite and correct that a little:

sub duplicate_record {
   my ($name, $surename) = @_;
   my $is_duplicate = 0;
   my $html_title = 'Duplicate records have been found!';

   open (DBFILE, "dbfile.pdb") or die("Cannot open file for matching: 
+$!");
   local $_;
   while (<DBFILE>) {
      my @pattern_check = split(/,/, $_); #spit line where you see com
+ma (,) ($record)
      if ($name eq $pattern_check[0] and $surename eq $pattern_check[1
+]) { #check if duplicate is available
         print $cgi->start_html($html_title).
               $cgi->h1('Duplicate records:').
               $cgi->p("$name $surename $phone already exists.\nGo bac
+k and fill something else than that!").
               $cgi->end_html;
         $is_duplicate = 1;
         last;
      }
   }
   close (DBFILE);

   save_db() unless $is_duplicate;
}
[download]

This should work better, let me make some remarks

• Don't use global variables, pass the relevant variables ($name and $surename) to your subroutine.
• use strict;
• put the important part first: open or die and not die unless open.
• use last, next and redo for loop control
• Readup how <FILE> behaves in scalar and list context.
• Think about better variable names: $found -> $is_duplicate. What does $name stand for? $firstname?

Update:

• As gjb points out, there might be a problem with not printing a HTTP header, too. I assumed in my snippet that this header is printed somewhere else before calling the sub.

-- Hofmator