You general approach is just fine. However, if you are always reading 2 lines at a time, why not just read them both in the while conditional? If there are an odd number of lines, below code will just throw away that last line that doesn't have a partner following it. The other question is what to do with blank lines at the end? Maybe somebody hit <cr> again a few times? Or mistake in cut-n-paste? I did something simple to allow for an undef resulting from split on "\n". Other implementations are of course possible, I don't know enough about your actual app.

I try to avoid stuff like $tmp[0] because you need a comment to describe what the heck the 0th field actually means! I used an array slice to move the indexing into the split so that I could assign this first column a scalar name. You should use terminology appropriate for your application. I didn't see the need for chomp, only to add a "\n" back in. The split will remove any \n if there is just one token on the line. Also, I personally wouldn't put multiple statements on the same line. Perl doesn't care, but people do.

I would do something different if this involved reading chunks of more than 2 lines. But this specific case, I find the below adequate.

use strict;
use warnings;

my $cnt=1;

while (defined (my $first = <DATA>) and defined (my $second = <DATA>) 
+) 
{
   
   my $name1 = (split /\s+/, $first)[0]  // last;  # handle trailing
   my $name2 = (split /\s+/, $second)[0] // last;  # potential "\n" bl
+ank lines
   
   print "$cnt\t$first";
   
   if ($name1 ne $name2) 
   { 
      $cnt++; 
   }

   print "$cnt\t$second";
}

=prints
1       one
1       one
1       two
1       two
1       three
1       three
1       three
2       four
note: same result with or without the trailing blank line
=cut


__DATA__
one
one
two
two
three
three
three
four
Odd line here followed by a blank line if you want
[download]

Update: Oh, I usually put the numbering on the left. I know how big that column is going to get. Done the other way around, a long token will screwup your nice printout. You didn't specify what is to happen with an odd number of line - it could be "silent ignore" approach above is not what you want - but I couldn't tell.

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