local $/="\$\n";
open(A, 'file');
while(<A>) {
   if (m/^(\w+)\n/) { #use whatever reges matches 'DATA' here
      open(my $fh, ">$1") or die "Couldn't open '$1' for write: $!";
      print $fh $_;
      close $fh;
   }
}