I think you have an off-by-one error. Change:

    for ( my $i = 0 ; $i <= @parts ; $i++ ) {
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to:

    for ( my $i = 0 ; $i < @parts ; $i++ ) {
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You probably need to chomp @Proto, then add the newline back to your @Assembly.

After using perltidy, here are the changes:

use warnings;
use strict;
use Text::ParseWords;

my @Proto  = <DATA>;
chomp @Proto;
my $Header = shift @Proto;
my @Assembly;

my $Nr   = &parsingHeader( $Header, "Number" );
my $Nr_1 = &parsingHeader( $Header, "Number_1" );
my $name = &parsingHeader( $Header, "Name" );

foreach (@Proto) {
    my @fields = quotewords( ';', 0, $_ );
    $fields[$Nr]   =~ tr/0123456789/9876543210/ if defined $Nr;
    $fields[$Nr_1] =~ tr/0123456789/9876543210/ if defined $Nr_1;
    $fields[$name] =~ tr/A-Za-z/B-Wzb-w/        if defined $name;

    push @Assembly, join( ";", @fields ), "\n";
}
unshift @Assembly, $Header;
print @Assembly;


sub parsingHeader {
    my $x;
    my $Row    = shift @_;
    my $Column = shift @_;
    my @parts  = split( /;/, $Row );
    for ( my $i = 0 ; $i < @parts ; $i++ ) {
        if ( $parts[$i] eq $Column ) {
            $x = $i;
            last;
        }
    }
    return $x;

}

__DATA__

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