Here is a way to do it using two hashes, %n_count to keep track of the number of times each name appears, and %f_count to keep track of the files in which each occurs. 
my (%f_count,%n_count);

for my $file (@files) {
    open( my $fh, '<', $file ) or die "Couldn't read '$file': $!";
    
    while (my $line = <$fh>) {
        chomp $line;
        next unless $line;
        my ($name,$number) = split(',',$line);
        $n_count{$name}++;
        $f_count{$name}{$file}++;
    }
}

[download]
Then you need to extract the names - first get the names that appear at least 25 times in the %n_count hash, then, for each of those candidate names, get the ones that appear in all files. 
my $num_of_files = scalar @files;
my $min = 25;
my @candidates = grep { $n_count{$_} >= $min } keys %n_count;

for my $name (@candidates) {
    my $in_files = scalar keys %{ $f_count{$name} };
    next unless $in_files == $num_of_files;
    print "$name\n";
}

[download]
The only tricky bit here is the scalar keys %{ $f_count{$name} }
$f_count{$name} is a hash reference, where each key is a file name. We can get at the keys by dereferencing the hash %{...} and counting how many there are. If that count equals the number of files then that name is in every file.

In reply to Re: Extracting common keys present in multiple files by tangent
in thread Extracting common keys present in multiple files by Anonymous Monk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.