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" blank 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