All you need to do is putting the names in a hash and print them out later (the quick fix) -

open (Mer, "Extracted.c")
%vars;
for $mer(<Mer>){
  $control=0;
  while ($control!=15){
    $mer =~ s/ //; 
    $control++;
  }
  $vars{$mer} = 1;
}
print "$_" foreach(keys %vars);
[download]

Another method is to use the hash to eliminate duplicates on the fly -

open (Mer, "Extracted.c")
%vars;
for $mer(<Mer>){
  $control=0;
  while ($control!=15){
    $mer =~ s/ //; 
    $control++;
  }
  next if $vars{$mer};
  $vars{$mer} = 1;
  print $mer;
}
[download]

The following is how I would do this -

use strict;
use IO::File;
my $Mer = new IO::File "Extracted.c", "r"
  or die "Can not open file!";
my %vars;
while my $mer (<$Mer>) {
...
}
[download]

Try to use IO::File to open a file in perl. It's the preferred method. ;-)