use the -f option on tail
from the man pages...

     -f    Follow. If the input-file is not a pipe,  the  program
           will  not  terminate  after the line of the input-file
           has been copied,  but  will  enter  an  endless  loop,
           wherein  it  sleeps  for a second and then attempts to
           read and copy further  records  from  the  input-file.
           Thus  it  may  be used to monitor the growth of a file
           that is being written by some other process.
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This is not perfect as per your specs but it does work.
Also, your while will then be infinite so you might need some condition to exit out of it.

update:
as ikegami points out your --follow=name is something (if not exactly) like the -f option. My system (sun) does not appear to have the same option.

another update:
here's an example of what ikegami is talking about...

use IO::Select;
open (F, 'tail -f somefile.log |') or die;
$select = IO::Select->new(*F) or die "Unable to create select object";
while(<F>) {
   $lastrec = "matt: ".$_;
   print $lastrec;
   while (! $select->can_read(1)) {
      print $lastrec;
   }
}
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