Your code (after the off by one error is fixed) does work, but you aren't getting much "mileage" out of ParseWords. I recoded without that below.

A few comments:
-don't push when you could print.
-there is no need to save all the output in an array.
-using a hash allowed me to get rid of variables like $Nr_1 and put code in same lingo as the file itself.
-this kind of "anonimization" is easily cracked - not so anon.
-you will need a better scheme if this data is sensitive.

#!/usr/bin/perl -w
use strict;

my $header_line = <DATA>;
print $header_line;
$header_line =~ s/\s*$//; # no trailing blanks or \n
                          # a bit better than chomp() here
                          # (chomp only gets rid of \n)
                          # since words will be hash keys             
+      

my %index;                # field name to index number

my $i=0;
foreach ( split /;/,$header_line )
{
   $index{$_}=$i++;
}

while(<DATA>)
{
    next if /^\s*$/;      # skip blank lines
    
    chomp;
    my @parts = split(/;/,$_);
    
    $parts[$index{Number}]   =~ tr/0123456789/9876543210/;
    $parts[$index{Number_1}] =~ tr/0123456789/9876543210/;
    $parts[$index{Name}]     =~ tr/A-Za-z/B-Wzb-w/;
    
    print join (";",@parts),"\n";
}

=output
Number;Name;Age;Gender;Number_1
876;Brhviw;54;m;876;AAA
765;Kslr;43;m;765;JJJ
654;Iipir;23;w;654;HHH
=cut

__DATA__
Number;Name;Age;Gender;Number_1
123;Andrew;54;m;123;AAA
234;John;43;m;234;JJJ
345;Helen;23;w;345;HHH
[download]