Your flag is working and breaking you out of your while loop just fine. However, you call your dirname() sub for every image found. If you put a line like the following at the beginning of your sub, you'll see what's happening:

print "Entering sub dirname\n";
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For readability, I'd get rid of the flag variable altogether by putting my test in the while condition. I also find it awkward to have a break out of the first half of an if-else with the major work in the second half. (Not wrong, just awkward.) So I'd do something like this:

sub dirname {
    print "Entering sub dirname\n";
    my $word = "site";
    my $counter = 1;
    my $name;
    do {
        $name = $word . "_" . $counter++;
    } while( -e $name);
    mkdir $name, 0755 or warn "Cannot make dir $name:  $!";
    print "$name \n";
}
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