Indent your code, it makes it a lot more readable and will help you to find errors. Use warnings and strict. Declare all variables. The fat arrow '=>' makes hash assignments more readable. Chomp assignments to save a line.

There was nothing wrong with what you posted except the shebang line. A bit of polish makes it a lot more maintainable.

Here is a cleaned up version:

#!/usr/bin/perl
use warnings;
use strict;

my %words = ( Sarah  => 'cat',
              Bob    => 'dog',
              Ronald => 'apple',
              Eric   => 'banana' );

print "What is your name?";
chomp (my $name = <STDIN>);

if ($name eq "Jerry") {
  print "Hi, Jerry!   Have a good day!\n";
} else {
  print "Hello, $name!\n";    #normal greeting
  my $secretword = $words{$name};    #get the secret word
  print "Guess the secret word.\n";
  chomp (my $guess = <STDIN>);
  while ($guess ne $secretword) {
    print "I'm sorry.   That is not the correct word.   Please try aga
+in.\nWhat is the secret word?";
    chomp ($guess = <STDIN>);
  }
}
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