First off, take a hard look at your nested loop. It may help to rewrite it a little to see what's going on:

    foreach $name (@name) {
        last if ($name =~ $filename);

        unlink($files . "\\" . $filename)
            or warn qq{cannot delete $filename: $!+};
        last;
    }
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which is the same as:

    if ($name[0] !~ $filename) {
        unlink($files . "\\" . $filename)
            or warn qq{cannot delete $filename: $!+};
    }
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because the two uses of last mean that you only ever get 1 iteration of the nested loop. That code ensures you delete the current file unless the first name happens to match the current file name.

However when you want to answer a "is it in the set" question use a hash. Consider:

#!\perl\bin\perl
use strict;
use warnings;

my $files = "C:\\Directory";
my $list  = "C:\\Test.sdf";

my %keepList;

open my $namesIn, '<', $list or die "Failed to open file: $!\n";

while (<$namesIn>) {
    chomp;
    $keepList{$_} = 1;
}
close $namesIn;

opendir my ($filesScan), $files;

while (my $filename = readdir $filesScan) {
    next if exists $keepList{$filename};
    
    unlink "$files\\$filename" or warn qq{cannot delete $filename: $!+
+};
}

closedir $filesScan;
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Note that I haven't tested the code!