As almut said, $ARGV hold the current file name, so you could get the number of lines for each file into a hash with:

while (<>)
{
   $lines{$ARGV}++;
   ...
}
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Or use the change in $ARGV to detect a new file, for example to print a banner:

while (<ARGV>)
{
   if ( $ARGV ne $current_file )
   {
      print "\n","-" x 20, " $ARGV ", "-" x 20, "\n";
      $current_file = $ARGV;
      $files++;
   }
   print;
}
[download]