The problem with your regexp is that since you're matching two backslashes, you need four in the regexp. I've condensed your code a bit; this should work for what you need.

open (PP, "net view |") || die "$!\n";
my @servers = map /^(\\\\[^lw].*?)\W/i, <PP>;
close PP || die "$!\n";

open (OUT,">servers.log") || die "$!\n";
print OUT join "\n", @servers;
print "List built!\n";
close OUT || die "$!\n";
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If you know for sure that net will be installed and working, you could shorten the first three lines to my @servers = map /^(\\\\[^lw].*?)\W/i, `net view`;