use strict; use warnings;! It'll find numerous errors including the fact that you use $Temp without ever assigning a value to it.

m//g in scalar context is almost always an error. It is here.

Your pattern will accidentally match keys "Named", "Names", etc.

use strict;
use warnings;

my $Profile = "C:\\registry.reg"; # unicode file
my $old_name = 'Foo';
my $new_name = 'Bar';

my @reg_file;
{
    open(my $fh, '<:raw:perlio:encoding(UTF-16):crlf', $Profile)
        or die("Can't open file $Profile: $!\n");
    @reg_file = <$fh>
}

for (@reg_file) {
    s/
        ^
        ( \[ HKEY_LOCAL_MACHINE\\SOFTWARE\\ )
        $old_name
        ( (?:\\.*)? \] )
    /$1$new_name$2/x;
}

{
    open(my $fh, '>:raw:perlio:encoding(UTF-16le):crlf', $Profile)
        or die("Can't overwrite file $Profile: $!\n");
    print $fh "\x{FEFF}", @reg_file;
}
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The weird stuff on the open line is to handle CRLF properly with UTF-16

Using UTF-16 instead of the real encoding (UTF-16le) removes the byte order mark, if I remember correctly. That's the odd character I print out at the end.

Ok, fine, I think the file is actually encoded using UCS-2le, not UTF-16le, but it's a subset of UTF-16le, so all's good.