If speed is important then a more complex single pre-evaluated regex may be faster for you. But it wasn't with this machine

my $regex=qr{(?:(?:\Q$nameOne\E).*(?:\Q$nameTwo\E)|(?:\Q$nameTwo\E).*(
+?:\Q$nameOne\E))};
if ($text !~ $regex) {
   print "$name\n";
   ++ct;
}
[download]

An Example benchmark test script (ugly but compares the two methods)

use Benchmark;
$n1='h';
$n2='e';
$r=qr{(?:(?:\Q$n1\E).*(?:\Q$n2\E)|(?:\Q$n2\E).*(?:\Q$n1\E))};

@i=qw(hello how are you doing are you going to exit now? each time?);
timethese (10000, {
var=> sub {
 for $w (@i) {
  $ct1++ if ($w!~$r);
 }
},
and => sub {
 for $w (@i) {
  $ct2++ if ($w!~ m/\Q$n1\E/ or $w !~ m/\Q$n2\E/);
 }
}
});

print "$ct1, $ct2\n";
[download]

Benchmark: timing 10000 iterations of and, var...
and: 2 wallclock secs ( 0.73 usr + 0.00 sys = 0.73 CPU) @ 13698.63/s (n=10000)
var: 1 wallclock secs ( 1.08 usr + 0.00 sys = 1.08 CPU) @ 9259.26/s (n=10000)
110000, 110000
Of course this benchmark figure is not based on real data so it is better to use it on the actual data to get a real indication.
Hope it helps
UnderMine