You may want to look at File::Find (see Beginners guide to File::Find) for a more elegant way to do this. And there is probably a better way to search for things in the file, such as slurping the whole thing into a single variable.

use File::DosGlob;
my $root =  '/some/where/interesting/*'; # don't forget the *!
my $name = 'Smith'; # what you are searhcing for
my @m = File::DosGlob::doglob(1,$root);
for $fn (@m) {
  if -d($fn) {
    push @m, File::DosGlob::doglob(1,$fn.'/*');
    next;
  }
#  uncomment to only search .txt files
#  next unless ($fn=~/\.txt$/);
  open (FILE,$fn) or warn "unable to search file $fn because $!\n";
  while (<FILE>) {
    next unless (index($_,$name) >=0); # you could use a regex here
    print "$fn: $_";
    last; # unless you want all occurences
  }
  close(FILE);
}
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Dingus