It is important to use copy and paste to post your code otherwise we end up chasing transcription errors. In this case while(<fhand>}{ is bad syntax and is probably a transcription error. But what about if($First = 1); (assign 1 to $first - the test is always true)? Transcription error or bug?

You should always add use strict; use warnings; to your code. They will catch many silly mistakes. In this case both the errors pointed out above would have been caught.

Of less importance in ($_ =~/ the $_ =~ is redundant.

You don't actually provide any test data and you don't say under what circumstances the result is incorrect. The followign code should serve as a starting point for elaborating on the actual problem you are having:

use strict;
use warnings;

while (<DATA>) {
  next if (m/First Name/ .. m/Last Name/);
  next if ! m/Last Name/;
  print "Order is not correct\n";
  last;
}

__DATA__
.......
Last Name
......
.......
First Name
.......
[download]

Prints:

Order is not correct
[download]