open(FH,'file.200207') or die 'hlpfl err msg';
while(<FH>) {
  # get name
  $name = (split /\s+/, $_)[0];
  # init count
  $info->{$name} = 0;
}

for('file.200204','file.200205','file.200206') {
  open(FH, $_) or die 'nther hlpfl err msg';
  while(<FH>) {
    # get name
    $name = (split /\s+/, $_)[0];
    # update count
    if(defined $info->{$name}) { $info->{$name}++ }
  }
}
[download]

Just a suggestion. Haven't tested it, so use with caution.

update: Hmm... I see fuzzyping has posted a very valid solution to your problem too ... only he keeps track of the name appearing in individual files, and I keep the entire sum. I didn't even think about that-- I don't know what you meant in your original post (it looks like it could go either way from re-reading it), but there's yet another disclaimer :)