Thanks
I've spent some time looking into these two methods for removing appenders but it turns out that you can only use them if you manually create the appenders (with Log::Log4perl::Appender->new) and add them (with $log->add_appender).
If you create your appenders via a configuration file (like I've shown above) then the logger object does not keep track of all the appenders by name.
I'm not sure if this is a 'feature' but it is the way it works with the version I have installed (1.05).
Here is an example with a configuration file

erickn@cofjora01d:/home/erickn> cat logtest1 
use strict;
use warnings;
use Log::Log4perl;
use Data::Dumper;

my $log_conf1 = <<EOT;
log4perl.rootLogger=DEBUG, Screen
log4perl.appender.Screen=Log::Log4perl::Appender::Screen
log4perl.appender.Screen.stderr=0
log4perl.appender.Screen.layout=Log::Log4perl::Layout::PatternLayout
log4perl.appender.Screen.layout.ConversionPattern = %d %-1.1p %P %H %m
+%n
EOT

Log::Log4perl->init(\$log_conf1);
my $log = Log::Log4perl->get_logger;
print Dumper $log;

$log->debug('this is a test');

erickn@cofjora01d:/home/erickn> perl logtest1
$VAR1 = bless( {
                 'is_OFF' => sub { "DUMMY" },
                 'is_DEBUG' => sub { "DUMMY" },
                 'ERROR' => sub { "DUMMY" },
                 'is_INFO' => sub { "DUMMY" },
                 'layout' => undef,
                 'category' => 'main',
                 'DEBUG' => $VAR1->{'ERROR'},
                 'is_ALL' => sub { "DUMMY" },
                 'additivity' => 1,
                 'ALL' => sub { "DUMMY" },
                 'is_FATAL' => sub { "DUMMY" },
                 'is_WARN' => sub { "DUMMY" },
                 'FATAL' => $VAR1->{'ERROR'},
                 'appender_names' => [],
                 'WARN' => $VAR1->{'ERROR'},
                 'INFO' => $VAR1->{'ERROR'},
                 'level' => undef,
                 'num_appenders' => 0,
                 'OFF' => $VAR1->{'ERROR'},
                 'is_ERROR' => sub { "DUMMY" }
               }, 'Log::Log4perl::Logger' );
2006/07/17 18:05:13 D 14011 cofjora01d this is a test
[download]

As you can see the object does not keep track of the appenders but still correctly writes output.

However, if I manually create the appenders like...

erickn@cofjora01d:/home/erickn> cat logtest2 
use strict;
use warnings;
use Log::Log4perl;
use Data::Dumper;

my $screen = Log::Log4perl::Appender->new(
   "Log::Log4perl::Appender::Screen",
    name      => "Screen",
);

my $layout = Log::Log4perl::Layout::PatternLayout->new("%d %-1.1p %P %
+H %m%n");
$screen->layout($layout);

my $log = Log::Log4perl->get_logger;

$log->add_appender($screen);

print Dumper $log;

$log->debug('this is another test');
erickn@cofjora01d:/home/erickn> perl logtest2
$VAR1 = bless( {
                 'is_OFF' => sub { "DUMMY" },
                 'is_DEBUG' => sub { "DUMMY" },
                 'ERROR' => sub { "DUMMY" },
                 'is_INFO' => sub { "DUMMY" },
                 'layout' => undef,
                 'category' => 'main',
                 'DEBUG' => $VAR1->{'ERROR'},
                 'is_ALL' => sub { "DUMMY" },
                 'additivity' => 1,
                 'ALL' => sub { "DUMMY" },
                 'is_FATAL' => sub { "DUMMY" },
                 'is_WARN' => sub { "DUMMY" },
                 'FATAL' => $VAR1->{'ERROR'},
                 'appender_names' => [
                                       'Screen'
                                     ],
                 'WARN' => $VAR1->{'ERROR'},
                 'INFO' => $VAR1->{'ERROR'},
                 'level' => undef,
                 'num_appenders' => 1,
                 'OFF' => $VAR1->{'ERROR'},
                 'is_ERROR' => sub { "DUMMY" }
               }, 'Log::Log4perl::Logger' );
2006/07/17 18:12:41 D 14290 cofjora01d this is another test
[download]

The appender is listed in the object and is available for removal or eradication.