Probably not very efficient, but just count them:

use warnings;
use strict;

my @names = qw(bob jan mike);
while (<DATA>) {
   my $cnt = 0;
   for my $name (@names) {
      $cnt++ if /\b$name\b/i;
   }
   print if $cnt == 3;
}

__DATA__
Mike went to the store with Jan.
Jan, Bob and Mike ate lunch.
In January, we bobbed for apples and sang into a mike.
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Prints:

Jan, Bob and Mike ate lunch.
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