Your test isn't runnable, so I had to adapt it a bit

#!/usr/bin/perl

use strict;
use warnings;

use Encode qw( encode from_to );

print("Content-Type: text/html; charset=utf-8\n\n");

my $name = encode('utf-16le', "\x{65E5}\x{672C}\x{8A9E}");
eval { from_to($name, 'utf-16le', 'utf-8', Encode::FB_CROAK); 1 }
    or print("coaked\n");

print $name;
[download]

It works fine. It displays "Japanese (language)" in Japanese.

From the prompt, I get:

$ test.cgi | od -c
0000000   C   o   n   t   e   n   t   -   T   y   p   e   :       t   
+e
0000020   x   t   /   h   t   m   l   ;       c   h   a   r   s   e   
+t
0000040   =   u   t   f   -   8  \n  \n 346 227 245 346 234 254 350 25
+2
0000060 236
0000061
[download]

Find what differs, and you'll find which bad assumption you made.

By the way, the following is a better model:

#!/usr/bin/perl

use strict;
use warnings;

use Encode qw( encode decode );

binmode(STDOUT, ':encoding(utf-8)');
print("Content-Type: text/html; charset=utf-8\n\n");

# Input
my $name = encode('utf-16le', "\x{65E5}\x{672C}\x{8A9E}");
eval { $name = decode('utf-16le', $name, Encode::FB_CROAK); 1 }
    or print("coaked\n");

# Process
# ...

# Output
print $name;
[download]