Here is some code for you, and I have comments along with it.

Two suggestions:

1. use strict all the time
2. always test with -w

use strict; # do this all the time

addbuddy("Peter1"); # the more test cases, the better
addbuddy("Peter2");
addbuddy("Peter1");
addbuddy("Peter3");
addbuddy("peTer 1");

sub addbuddy {
    my $victim = shift;
    $victim =~ s/ //g; # transform victim in the same way you transfor
+m the list, otherwise you may run into trouble without your notice
    $victim = lc($victim);

    open(FILE, "<", "names.txt"); # I don't want use +< to confuse you
+, even though it is better for this case
    my @list = <FILE>; #read in the whole list
    close(FILE);

    foreach my $item (@list) {
        chomp($item); #get rid of line breaks
        $item =~ s/ //g;
        $item = lc($item);
    }

    my %list = map {$_, 1} @list; # the only thing looks tricky in my 
+code
    if (!defined($list{$victim})) {
        open (DATA, ">>names.txt");# you don't want to use >, and over
+write your file.
         print DATA "$victim\n";
         close (DATA);
        print "Buddy $victim was added\n";# always make the debug msg 
+meaningful
    }
}
[download]